{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 13: Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Robert Johansson\n",
    "\n",
    "Source code listings for [Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib](https://www.apress.com/us/book/9781484242452) (ISBN 978-1-484242-45-2)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sns.set(style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Descriptive statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([3.5, 1.1, 3.2, 2.8, 6.7, 4.4, 0.9, 2.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9, 6.7)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.min(), x.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0700000000000007"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7521415467935233"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5085714285714293"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.var(ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8731181032095732"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std(ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6414006161858726"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.random()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.randint(0, 10)  # 0 and 10 inclusive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.532833024789759"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8768342101492541"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.71356403, 0.25699895, 0.75269361, 0.88387918, 0.15489908])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.13325952,  1.15727052,  1.37591514,  0.94302846],\n",
       "       [ 0.8478706 ,  0.52969142, -0.56940469,  0.83180456]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 8, 3, 9, 0, 6, 9, 2, 7])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(10, size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 18, 18, 17, 14, 12, 14, 10, 16, 19],\n",
       "       [15, 13, 15, 18, 11, 17, 17, 10, 13, 17]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=10, high=20, size=(2, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
    "\n",
    "axes[0].hist(np.random.rand(10000))\n",
    "axes[0].set_title(\"rand\")\n",
    "axes[1].hist(np.random.randn(10000))\n",
    "axes[1].set_title(\"randn\")\n",
    "axes[2].hist(np.random.randint(low=1, high=10, size=10000), bins=9, align='left')\n",
    "axes[2].set_title(\"randint(low=1, high=10)\")\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-random-hist.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#random.sample(range(10), 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 0, 5, 8, 1])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(10, 5, replace=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.532833024789759"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.532833024789759"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123456789); np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.532833024789759"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123456789); np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "prng = np.random.RandomState(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.212902  ,  2.1283978 ,  1.8417114 ,  0.08238248],\n",
       "       [ 0.85896368, -0.82601643,  1.15727052,  1.37591514]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.randn(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.26859720e+00, 2.02731988e+00],\n",
       "       [2.52605129e-05, 3.00376585e-04]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.chisquare(1, size=(2, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.59734384, -1.27669959,  0.09724793],\n",
       "       [ 0.22451466,  0.39697518, -0.19469463]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.standard_t(1, size=(2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.77372119,  0.1213796 ,  1.64779052,  1.21399831],\n",
       "       [ 0.45471421, 17.64891848,  1.48620557,  2.55433261]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.f(5, 2, size=(2, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 3, 4, 2, 4, 5, 4, 4, 7, 5])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.binomial(10, 0.5, size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 1, 3, 4, 6, 4, 9, 7, 3, 6])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prng.poisson(5, size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability distributions and random variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = stats.norm(1, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 1.0, 1.25, 1.75, 2.6875]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[X.moment(n) for n in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(1.), array(0.25))"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.10798193, 0.79788456, 0.10798193])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.pdf([0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02275013, 0.5       , 0.97724987])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.cdf([0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.106451  , 2.0641989 , 1.9208557 , 1.04119124, 1.42948184,\n",
       "       0.58699179, 1.57863526, 1.68795757, 1.47151423, 1.4239353 ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.rvs(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(1.), array(0.25))"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm(1, 0.5).stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(2.), array(0.25))"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.stats(loc=2, scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.020018007729972975, 1.979981992270027)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.interval(0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.2879146517744502, 2.28791465177445)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.interval(0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_rv_distribution(X, axes=None):\n",
    "    \"\"\"Plot the PDF, CDF, SF and PPF of a given random variable\"\"\"\n",
    "    if axes is None:\n",
    "        fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
    "    \n",
    "    x_min_999, x_max_999 = X.interval(0.999)\n",
    "    x999 = np.linspace(x_min_999, x_max_999, 1000)\n",
    "\n",
    "    x_min_95, x_max_95 = X.interval(0.95)\n",
    "    x95 = np.linspace(x_min_95, x_max_95, 1000)\n",
    "\n",
    "    if hasattr(X.dist, 'pdf'):\n",
    "        axes[0].plot(x999, X.pdf(x999), label=\"PDF\")\n",
    "        axes[0].fill_between(x95, X.pdf(x95), alpha=0.25)\n",
    "    else:\n",
    "        x999_int = np.unique(x999.astype(int))\n",
    "        axes[0].bar(x999_int, X.pmf(x999_int), label=\"PMF\")\n",
    "    axes[1].plot(x999, X.cdf(x999), label=\"CDF\")\n",
    "    axes[1].plot(x999, X.sf(x999), label=\"SF\")\n",
    "    axes[2].plot(x999, X.ppf(x999), label=\"PPF\")\n",
    "    \n",
    "    for ax in axes:\n",
    "        ax.legend()\n",
    "    \n",
    "    return axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 3, figsize=(12, 9))\n",
    "\n",
    "X = stats.norm()\n",
    "plot_rv_distribution(X, axes=axes[0, :])\n",
    "axes[0, 0].set_ylabel(\"Normal dist.\")\n",
    "X = stats.f(2, 50)\n",
    "plot_rv_distribution(X, axes=axes[1, :])\n",
    "axes[1, 0].set_ylabel(\"F dist.\")\n",
    "X = stats.poisson(5)\n",
    "plot_rv_distribution(X, axes=axes[2, :])\n",
    "axes[2, 0].set_ylabel(\"Poisson dist.\")\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-distributions.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_dist_samples(X, X_samples, title=None, ax=None):\n",
    "    \"\"\" Plot the PDF and histogram of samples of a continuous random variable\"\"\"\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
    "\n",
    "    x_lim = X.interval(.99)\n",
    "    x = np.linspace(*x_lim, num=100)\n",
    "\n",
    "    ax.plot(x, X.pdf(x), label=\"PDF\", lw=3)    \n",
    "    ax.hist(X_samples, label=\"samples\", normed=1, bins=75)\n",
    "    ax.set_xlim(*x_lim)\n",
    "    ax.legend()\n",
    "    \n",
    "    if title:\n",
    "        ax.set_title(title)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rob/miniconda3/envs/py3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n",
      "/Users/rob/miniconda3/envs/py3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n",
      "/Users/rob/miniconda3/envs/py3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
    "X = stats.t(7.0)\n",
    "plot_dist_samples(X, X.rvs(2000), \"Student's t dist.\", ax=axes[0])\n",
    "X = stats.chi2(5.0)\n",
    "plot_dist_samples(X, X.rvs(2000), r\"$\\chi^2$ dist.\", ax=axes[1])\n",
    "X = stats.expon(0.5)\n",
    "plot_dist_samples(X, X.rvs(2000), \"exponential dist.\", ax=axes[2])\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-dist-sample.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = stats.chi2(df=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_samples = X.rvs(500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df, loc, scale = stats.chi2.fit(X_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.728645123391404, 0.03257330219133387, 1.0734482977974253)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df, loc, scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y = stats.chi2(df=df, loc=loc, scale=scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 3))\n",
    "\n",
    "x_lim = X.interval(.99)\n",
    "x = np.linspace(*x_lim, num=100)\n",
    "\n",
    "ax.plot(x, X.pdf(x), label=\"original\")\n",
    "ax.plot(x, Y.pdf(x), label=\"recreated\")\n",
    "ax.legend()\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-max-likelihood-fit.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FT1+l8Pt1dd1PvN3tWfLkCABe/sc+Ci5VWuSYhBBCiKtVVtfy1Y/nGd7Xt0Uu3o0b2oWR/f3YfeISFy6WWHz/QgjRFFJQtaKikipWbU6kd5A7kUN9yf54IYaii/g++Md6855ul61vV/x//QaO/cdQ/MN68uJWYK41ABDg7cTi2BGUVRr484eHqDZIty8hhBCW9fWhC5RVGnhgTI8W2b9KpeLpBwZgo1WxanOiLAUgxG3qiP8PWfKYpaBqRZ98fYqqmlqefXAABdtWYijMxvdXf8S+2wCLf5Zaa4PXpGdwu+shyhK/I/uTJRgrywAIDnDl/2YM5kx6MSvWHeuQ/xMJIYRoGUajiS3fnaV3kDshQS3XOMLF0Zax/V04fiaf/YnZLfY5QrR3er2egoKCDvV70Gw2U1BQYLF1qmQOVSvJLazg64MXuGdYIM7pP1KQvB/3sY9gFxjaYp+pUqlwGzUVras3eV/+neyPX8Zv5mI09s6M6OfHI/f2ZvW2ZLQmZ4YMabEYQgghOpC9x7PILapkzpR+Lf5Zg7s7cDLTxL++SGJwbx9sdZoW/0wh2puAgAAyMjLIy8tTOgoANTU12NjYtPjn6PV6AgICLLIvKahayfpdpwEVMf20FGz6D/bdB+MSNrlVPtspNByNvQs5618je+2f8Ju5CI2dE9PG9SDtYim7jmYw8qeLDOvr2yp5hBDCkuLi4li5ciW1tbXMnj2bmTNn1ns9OTmZBQsWUF5ezpAhQ1i8eDFarZasrCzmzZtHQUEBXbt2ZdmyZXWt5gEuXrzI5MmT2bRpk8VOuu2d2Wxm054UArwdGdqn5c8pGrWKOVP68ceVP7JpTwoPTejV4p8pRHuj0+no2rWr0jHqJCQkMGCA5UdvtSQZ8tcKLhaU882hNCYN9aHmm3fROLriFfVsvUV4W5p9twH4THuRmvx0stf+CWNlGSqVimd/NRA/dx1vf3KEnMKKVssjhFDWO++8Q3x8fJPe06uX9f1YzcnJYfny5axdu5bNmzezbt06UlJS6m0zb948Fi5cyI4dOzCbzaxfvx64vFbXjBkz2L59O6Ghobz33nt17zGZTCxYsACDwdCqx9PWHT+Tx7msS9x/d3fUast19ruVft09GTWgExt3nSZXzmNCCAU06hd9XFwckZGRTJgwgTVr1tx0u/nz59etUny1kydPEhrackPbrN2nX59Co1YRYXuE2kv5+Nz/f2jsW79luX3wIHynzqcmN42LnyzBVFOJrU7DtFEemM1m3lh9GEOtqdVzCSFa3+HDhzEa235Tmn379hEWFoarqyv29vZERESwffv2utczMzOpqqpi4MCBwOUFIbdv347BYODw4cNERETUe/6KDz74gJEjR+Lm5ta6B9TGfX0wDSd7G8YMbt07eo9F9QWVitXbklv1c4UQAhox5O/K1b9NmzZhY2PD9OnTGT58ON27d6+3zaJFi9i/fz9hYfW71VVWVrJkyZIOe5Uvv8TAnvgcpg91oiZpF86D7kEfoNxVXvvug/F54PfkbHyDnE1v4/vgH3B31PLbXw1i6X8P858vfyK2Fca9C6G00hPfUnp8d8Mb3oDRaOSS5uZzNZwGjMWp/90N7ufgwYO8+eabmEwm/P39sbe358yZMxiNRmJjY5k0aRLV1dUsXryYhIQEdDodTz/9NJGRkYwdO5b+/fuTnJzM2rVr+eGHH/jvf/+LyWSib9++/P73v8fBwYGPP/6YLVu2UFlZiU6n46233uLEiRMkJSXx0ksv8e6776LX63nllVcoLi5Gr9fz8ssv06dPHzIyMpg3bx4VFRVWO/wiNzcXLy+vusfe3t6cOHHipq97eXmRk5NDUVERjo6OaLXaes8DJCUlceDAAT744INbXkS8laSkpFu+npCQ0Kz9tqamZqypNbE/MZv+Xe05cfxYC6W63pWcQ7vb8e2RDPr4GfB20bXa5zdGe/z7VoJktAzJaHkNFlRXX/0D6q7+zZ07t26buLg4xo0bV7fN1ZYuXcrs2bM5cuSIBWO3Hd8nlaLTqbmz5ntMtna43TVd6Ug49ByK58RY8re9T/72VeA9hDv7dyJqdDe++OEcocEejOjXSemYQnQIqamp7Nmzh/fffx9vb29ef/11ysrKmD59OgMGDGDHjh1UVFSwbds2CgoKePTRRxk/fjwA4eHh/PWvf+XMmTOsX7+eTz/9FFtbW9566y1Wr17N448/zjfffMPq1avR6/X87W9/Y82aNbz88st89tlnzJ07l169ejF9+nQWLlxInz59SElJ4ZlnnmHHjh0sWbKEmJgYpk2bVjecztqYTKZ66/eZzeZ6j2/2+rXbweVGPpWVlSxevJi//e1vqNXNH5YdGhqKra3tDV9LSEhg8ODBzd53a2hOxu+OZGAwZvHAhIH0C/ZsoWT1XZ2ze69qjvzla45naPjDWOv5ftvr33drk4yWIRlvrbq6usELYjfSYEHV0NU/gCeeeAK4vprctWsXVVVVTJw4scnBoOErfDf6TGtSVmUkKa2C6C551KYlUhEynmPJZ5SO9QsP9N1GwtGvse1pIEGlYkAnMwnuOt5eE89T9/ngYm9dPUus+e/6CsloGS2VUavVUl5eDoA6eCguwUNb5HOAus+5laqqKgIDA1Gr1ezdu5eqqio2bNhQ9/7ExET279/PAw88QGVlJfb29qxfvx6DwYDJZKJHjx6Ul5fz/fffk5qaytSpUwEwGAyEhISgUqlYsmQJmzZtIi0tjX379tGzZ0/Ky8sxGo1UVVWRl5dHYmIiL774Yr3smZmZHDx4kCVLllBeXs64cePqfX9Xq6mpUey/K19f33pzwfLy8vD29q73+tWdq/Lz8/H29sbd3Z3S0lKMRiMajabuffHx8RQUFPDUU08Bl8+Bc+bM4d1336Vbt26td2Bt0PdHM/Fw0dO3q4cin+/iaMvk0cGs++Y05zIv0c3fRZEcQoiOp8FfzA1d/buZvLw8Vq5cyX/+859mh7vVFT6w/ip74+4zqEwZ3M0RdB7+9J0Si0pjPUWK+Y5B5G3RwE/fEtT3Dhz73EnnbmU899a37P6plj/NGdZqk4obYu1/1yAZLaUlMyYnJ9fr4tZc5eXlFtmPXq/H3t6+bl9vvfUWffv2BS7/8HdxceGrr75Cr9fXbXPhwgX8/PxQq9W4ubnh4OCAVqslMjKSl156qS5faWkpJSUlPPbYYzz88MOMGzcOPz+/uu9Ao9Gg1+vR6/XY2toSFxdXl+vixYv4+PigUqmws7PDwcEBs9mMRqO54XHb2NhcNySwuVf5mmrkyJGsWLGCwsJC7Ozs2LlzJ0uWLKl73d/fH1tb27r/rrZs2UJ4eDg6nY4hQ4awdetWoqKi2Lx5M+Hh4YwePZrdu/83FHTs2LH885//lC5/DSitqOHIqRwmjeqm6Hljyl3BfLn3HGt3/MxLvx6uWA4hRMfS4HiGa6/uXXv172a+/fZbiouLmTlzJtHR0QBER0dTVlZ2G3HbDpPJzPb9qUz2TIGSHDzGP2pVxRSASqXGa9IzGNwCyIt7l+qcVDp5OvJEdCjHz+QTt/ec0hGF6DDCwsL45JNPgMt3RSZPnkx2djZDhw5l69atdYsQPvzww9TU1NR77/Dhw/n666/rFmZ85ZVXWLNmDYmJiQQGBvLoo4/Sr18/vvnmm7pGFBqNBqPRiJOTE0FBQWzZsgWAH3/8sa7t+MiRI/niiy8A2LlzJ9XV1a31dTSaj48PL7zwArNmzWLKlClMmjSJ/v37ExsbS2JiIgDLli3jtddeY+LEiVRUVDBr1iwAFi1axPr164mMjCQ+Pp7nn39eyUNp0/adyKLWaOauQcoWno72Ntx/d3cO/nSR02lFimYRQnQcDf7Cb+jq381MmzaNadOm1T3u1atX3Qm7IzhyKpfCwhJGep3ArusA7LvfoXSkG1JpdZQPjEF/+GNyNr6O/6/fYMLwQA6fzOG/X51kYE8vAn2dlY4pRLs3d+5cXnnlFSZNmoTRaGTevHl06dKFGTNm8OqrrzJ58uV1615++WUcHR3rvTckJIS5c+cye/ZsTCYTvXv35rHHHsPW1pZPPvmEyMhIzGYzQ4cO5cyZy8OOR48ezaJFi3j99dd58803eeWVV/jggw/Q6XQsX74clUrFwoULmTdvHuvWrSM0NNQid+VaQlRUFFFRUfWeW7VqVd2fQ0JC2Lhx43Xv8/f3Z/Xq1bfc99V3q8TNfX80k06eDgQHKD/MLmp0N7Z8f441O35mcewIpeMIITqABguqq6/+GQwGpk6dWnf177e//S39+klHuBvZvj+VcOc0bIyVuN4Zo3ScWzLbOuIzdR5Zq18md/NyfH+1gLnTBvLssj28veYIy54LR6eVJcuEsLThw4czfPjlYUmOjo4sW7bsum1sbGz405/+dN3z1/7Qv/Yi1pVhiR9++OENP/vxxx/n8ccfr3t8o8LCx8eHjz76qO7xX/7ylwaOSHREBZcqSTybz6/G92rUlICWZq/XETOmO//96iQp6cV073x9wywhhLCkRv1KjoqK4ssvv2THjh3ExsYCl6/+XVtMLV26lJiYGxcPp06dus2obUduUQXxJ7MZ75BMrbMv+i59lY7UIL1/TzwjYqk8d5zCb9fi6mTLsw8O5FzWJdZ903H+7oQQQjTN3uNZmM0QPshf6Sh17h0RhL1ey2d7rKURlBCiPZPbDi1g54EL9NWlY19dQFXXMKu4YtcYzoPG4zToHi7t30zFmQSG9fVl7JDObNx1hnOZl5SOJ4QQwgr9cDSTbp1c6OzT+gvW34yDnY57RwSx70QW2fkNd9wUQojbIQWVhdUaTew8eIEotzNoXbwx+IQoHalJPCb8GhvvIHLjVlBbUsAT0aE4O9jw10+PUGs0KR1PiNtmNpuVjtCuyPfZsV0qq+Z0ehFh/fyUjnKdyeHBqNVqPv82RekoQoh2TgoqCzt2Og+Xygy8DZm4DJ8Et7EwpBLUWhu8Y36HudZA7ublOOo1PD11AOezStiwS4ZOiLZNo9FgMBiUjtGuGAwGtFrr6mAqWs/R03mYzTA4pOHuv63N3VnPuKGd+eZwGkWlVUrHEUK0Y23r134b8MOxTO6xP4la74DTgLFKx2kWG49OeEY+SVV6MkXffUpYqB/hg/xZ/80pUrNLlI4nRLO5urqSk5ODySR3Wy3BZDKRk5ODi4vynd2EMo6eysXJ3obgAOts/HD/3d2pNZqI+0GWARFCtBy5rGhBhlojp346zWS7CzjfEYPaxk7pSM3mFBpOVWoSxfs+xy6oH3Om9OP4mTzeWXeUN38bjsZKFvwVoik8PT3JyMi47SY5NTU12NjYWChVy2itjA4ODnh6erb45wjrYzKZOXIql0E9vaz2nODv5ciIfn5s/fE8U8f2wF6vUzqSEKIdkoLKgo6eyiPUfBpQ4XzHBKXj3DaPiMepykgmN24FAbFvExvdj2VrEvjqx3NMHh2sdDwhmkytVtOlS5fb3k9CQgIDBgywQKKW0xYyirYtNbuE4tJq7rDC4X5Xe2BMD/adyGbnwTSm3CXnLiGE5cmQPwv64WgGYfpz6AND0bp4KR3ntql1tnhHP4+x/BL5295n9MBO3BHizcfbkskrqlQ6nhBCCAUdOZULwKBe1l1Q9eziRu8gd77cew6jSZqoCCEsTwoqC6k2GMn9+Rju6lKcB9ytdByLsfULxv2u6ZQn76c86XueiumPyQz/2HRCunsJIUQHduTnXIL8nHF31isdpUGTw7uRU1jB4ZMXlY4ihGiHpKCykCM/5zBAfQaz1haHXmFKx7Eol7Bo9J17k7/jAzw0ZcyYEMKhkxfZl5itdDQhhBAKqKgykJxaYJXd/W5kRKgfnq520pxCCNEipKCykH1HUhlkcwHH3iNR21j/1bqmUKk1eEX/FlQq8r5YweTRQXTr5MI/Pz9BeaW0oBZCiI4mMSWfWqPZ6of7XaHRqLnvzq6cSMnnfJYsVC+EsCwpqCygqrqW6pRD2KoMOA8co3ScFqFz8cZzwq+pSk+mLGEbcx8cQFFpNWt2/Kx0NCGEEK3syKlc9DYa+nR1VzpKo0WEBWKj08hdKiGExUlBZQGHk3MYpDmDycETfefeSsdpMY797sa+xxCKvl0+7ucfAAAgAElEQVRLoH0F944I4qu950jJKFY6mhBCiFZ09FQe/bp7otNqlI7SaE72NowZHMB3RzK4VFatdBwhRDsiBZUFnDh2ih7ai7gNGotK1X6/UpVKhWfkb1DpbMj7YgUPT+yFs6MtKz87Lp2ThBCig8jKLyO7oJzBbWS439WiRnejptbEzoMXlI4ihGhH2u+v/1ZiNJnRpB5EraJddfe7Ga2jG54RsVRnncF4fCuPR/XldFoxOw+kKh1NCCFEK0g6WwBA/x5tb3mQQF9nBvbwYuu+VIxGk9JxhBDthBRUt+lMehEhqvNUuwaic/VROk6rcOhzJw69R1D43TpGdDbTv7sn/92aTFFpldLRhBBCtLDk84U42dsQ4O2odJRmibyzK/nFlRxOzlE6ihCinZCC6jYlHj9NF20B7n1HKB2l1ahUKjwjYlHr7cn/6j2enBJKdU0t//nypNLRhBBCtLCT5wvo09UdlUqldJRmGdbHB08XPVt/PK90FCFEOyEF1W0qPXUIALfQjlNQAWgcXPCc8DjVWWdwvvAd0eHB7I5P5+T5AqWjCSGEaCHFpdVk5Ze3qe5+19Jo1ESMCOLo6Tyy8suUjiOEaAekoLoNRaVV+JWfplLvhY1ngNJxWp1Dnzux7zGUou8+4YEhzni66PnHphMyLl0IIdqp5NTLF836dPVQOMntmTA8EI1axbZ9qUpHEUK0A1JQ3YbjSal0115E332o0lEUoVKp8Lx3DiqNltKd7/P45D6czyph2/5UpaMJIYRoASfPF6LTqgkOcFE6ym1xd9Yzop8f3xxKo9pgVDqOEKKNa1RBFRcXR2RkJBMmTGDNmjU33W7+/Pls2rSp7nFCQgJTp04lOjqa2bNnk5mZefuJrcjF4wfQqMx0umOU0lEUo3Vyx+Oex6hKT6afIZEBPTz5eFsyxaWyxocQQrQ3yecL6dnFrU2tP3UzkXd2pazSwA9H29dvEyFE62uwoMrJyWH58uWsXbuWzZs3s27dOlJSUq7b5je/+Q07duyo9/y8efN49dVX2bJlC1FRUbz66quWTa8go9GEfW4iVRpH9AE9lI6jKMf+Y7Dr2p/Cb9cy5x5/qmqM/PcraVAhhBDtSVVNLSkZxfQOarvzp64W2s2Dzj5ObNsvzSmEELenwYJq3759hIWF4erqir29PREREWzfvr3eNnFxcYwbN45777237rmamhqee+45QkJCAOjVqxfZ2dkWjq+c0+dy6aHOwBgwsF0v5tsYl4f+PQlmEzbxa4ke3Y1vDqdx6kKh0tGEEB1AQ6MokpOTiYmJISIiggULFlBbWwtAVlYWM2fOZOLEiTz11FOUl5cDkJKSwvTp05k8eTKPPPJIuxtd0Vxn0osxmsxtuiHF1VQqFZEjgzidVkxKRrHScYQQbViDlUBubi5eXv9bvM/b25ucnPprNzzxxBNMmzat3nM2NjZER0cDYDKZePfddxk/frwlMluFswn7sVXV0mnwaKWjWAWdmy9ud02nIiWByYGFuDvb8v7niZhMZqWjCSHascaMopg3bx4LFy5kx44dmM1m1q9fD8DixYuZMWMG27dvJzQ0lPfee6/u+aeffpovvviCyMhI3n777VY/Lmt0pYtrSDu5QwVw9+DO2Og07DhwQekoQog2TNvQBiaTqd5aE2azuUlrT9TU1PCHP/yB2tpannzyySaFS0pKanCbhISEJu3TUgwph6hW6UgtM5HaQAalMjaFRTKq/XBy9qNo5yrGhTzChkPF/GvjD9wR7HD7+6YDfY8tTDJahmS0DlePogDqRlHMnTsXgMzMTKqqqhg4cCAAMTExvPPOO0ybNo3Dhw/z97//ve75hx9+mHnz5vHhhx+i1WoxmUxkZWXh7OyszMFZmeTzhXTxdcLJ3kbpKBbjaKcjfKA/3x1J57FJfbDX65SOJIRogxosqHx9fYmPj697nJeXh7e3d6N2Xl5ezlNPPYWrqysrV65Ep2vaP1ShoaHY2tre9PWEhAQGDx7cpH1aQkl5Fdqtb1Pm0ZuhQ4fdclulMjaFJTNWd/Ei81/zmGh/mqSgAXz3UxkPRY3A0e72TlId7XtsKZLRMiRjw6qrqxt1Uex23WgUxYkTJ276upeXFzk5ORQVFeHo6IhWq633PIBWq6WkpITIyEiqqqpYvXp1k3M1dOxtodi9OqPJbCbpbB6hgfZWl/128wS6VfNNtZGPt+xjcHdHC6Wqz9q+sxuRjJYhGS2jLWS8WoMF1ciRI1mxYgWFhYXY2dmxc+dOlixZ0qidz5s3j8DAQBYvXoxa3X7mGZ0+loi7uoqantb9g0oJtj5BuI6YQvG+TTw5YTAvrKvhkx0/Ezuln9LRhBDtUEOjKG72+o1GW1z92NnZmb179/L999/z1FNPsWvXLjSaxne2u9UFQaWL3ca4NmNqdgnVhkzCh/Zi8ODOCiarzxLf5R1mM7sSvyU5y8ycX1n+76Ut/n1bI8loGZLx1pp7MbDBKsfHx4cXXniBWbNmMWXKFCZNmkT//v2JjY0lMTHxpu87efIku3bt4siRI9x///1ER0cTGxvb5IDWqODny1Vz4B3DFU5inVxHTUXr5ovu8MdEDvPnyx/Pc+FiidKxhBDtkK+vL3l5eXWPrx1Fce3r+fn5eHt74+7uTmlpKUaj8br3bd26FbP58vzP8PBwqqqquHTpUmscjtW6Mn+qvTSkuJpKpWJiWCApGZdISZfmFEKIpmvwDhVAVFQUUVFR9Z5btWrVddstXbq07s99+vTh1KlTtxnPOulyT1Gk8aCbm1fDG3dAap0tXvc+SfbaxUT3SOY7Ww9WbU5kyZMjmzT/TgghGtLQKAp/f39sbW3rrnhu2bKF8PBwdDodQ4YMYevWrURFRbF582bCw8MB+Pe//41Wq2XChAkcOHAANzc33N3bXyHRFMmphbg52eLjbq90lBZx1+DO/PvLk2w/kMrczgOVjiOEaGPazzi8VlJaUkYnYybVHj2VjmLV7Lr2x7Hf3VTGx/H4aFeOn8lnf2L7aZsvhLAOjRlFsWzZMl577TUmTpxIRUUFs2bNAmDRokWsX7+eyMhI4uPjef7554HLFwc//PBDoqOjeffdd3nnnXcUOz5rkZJeTM8ubu32otiV5hTfH82gosqgdBwhRBvTqDtU4n/OJCTgqjLi2usOpaNYPY/xs6lISaB3dhxBvvfwry+SGNzbB1td4+chCCFEQxoaRRESEsLGjRuve5+/v/8NG050796dTz75xPJB26iKKgOZeWXcdUeA0lFaVMSIQL45nMb3RzOZOCJI6ThCiDZE7lA1UfHpoxjNKrrdcevufgI09s543PMo1ZmnebpfEblFlXz+bUrDbxRCCGE1zmVewmyG7gGuSkdpUb26uBHk58yOg7ImlRCiaaSgaiJ94SnydJ3QO7ZMa9X2xjH0LuyC+mGXtJlxoc5s2HWG3KIKpWMJIYRopJSMyw05ggNcFE7SslQqFfcM70JKejHnMjt2ExIhRNNIQdUEJYVFeBtzqfUOUTpKm6FSqfC8dw7mWgMxdocB+DDuJ4VTCSGEaKyU9GI8XfS4OemVjtLixgzujE6rZqfcpRJCNIEUVE1wLn4/ahV49LHu/v3WRufeCddRU6k9e5DHBxnZezyLxLP5SscSQgjRCCkZxQS38+F+VzjZ2zCyXye+TUin2mBUOo4Qoo2QgqoJSs8ep8qso/vAQUpHaXNcR0Sj8wygb+42OrlpWbU5EaPJrHQsIYQQt3ClIUWPzh2joAKICAukvKqWH49nKR1FCNFGSEHVBI5Fp7lo0xlbWxulo7Q5Ko0Oz3ufxFiSxzPBqZzPKmHngVSlYwkhhLiFs5lX5k91nIIqNNgDP08HGfYnhGg0Kaga6VJ2Bi7mEsx+fZSO0mbZdemD08DxOJ7/lrsCzaze9jNlFTVKxxJCCHETZzOKgfbf4e9qKpWKCcMD+elcARm5pUrHEUK0AVJQNdKFY5cbKnj3kfWnbof72IdR2zkSo/+Rispq1uz4WelIQgghbuJMejGerna4OtkqHaVVjRvSGY1axdcH05SOIoRoA6SgaqTyCycpM9nSva/cobodGjsnPO55DPLO8URIAVv3pXIhu0TpWEIIIW7gbEYx3dt5u/QbcXPWM6yvL7vi0zDUmpSOI4SwclJQNZK+6Dw52k7Y6XVKR2nzHPuOxq5rf/oW7cFHX8M/NydiNkuDCiGEsCbllQYy88rp3oEaUlxtwvBALpXVcPjkRaWjCCGsnBRUjVBTWoyLqQiDR7DSUdoFlUqF58Q5YKzl6c4nOZGSz77EbKVjCSGEuMqVxW070vypqw3q5Y2ni16aUwghGiQFVSNk/XQUAJeuMtzPUnTufriOmopz3nHu9i7k318kyZofQghhRc6kd7yGFFfTqFWMG9aFI6dyySuqVDqOEMKKSUHVCAVnkjCY1QT26690lHblytpU0Tb7KS4qYdOeFKUjCSGE+MXZjGK83OxwcexYDSmuds+wQAC+OSzNKYQQNycFVWPkniHT5IW/T8e8StdSrqxNpa4o4PHAc2zcfYbcogqlYwkhhABSMoo77N2pK3zc7RnQw4uvD12QxeiFEDclBVUDTIZqnKuyKXUKRKVSKR2n3bmyNlVI2WH81IX8O+4npSMJIUSHV2UwkZVfTnAH7PB3rQnDA8krquT4mTylowghrJQUVA24lJqMBhM2/iFKR2m3rqxNNcf7CPuOZ3IiRU5aQgihpNxiAwBdO0lBFRbqi5O9DV9LcwohxE1IQdWAiyePA+DbW+ZPtZQra1M5lqcz0f08//w8EaNR1v0QQgil5PxSUAX5OSucRHk6rYaxQzpzICmbS2XVSscRQlghKagaUJn+M9m1rvToHqB0lHbtytpUE7TxFOXk8NW+80pHEkKIDiun2ICDXouXq53SUazCPcO7UGs0sychQ+koQggr1KiCKi4ujsjISCZMmMCaNWtuut38+fPZtGlT3eOsrCxmzpzJxIkTeeqppygvL7/9xK3IbDJiX5JKjk0nHO1kQd+WdGVtKg0mHvc5ztrtP8uVQCGEUEhOsYGgTi4yd/gXgb7OhAS6sfPgBVmIXghxnQYLqpycHJYvX87atWvZvHkz69atIyUl5bptfvOb37Bjx456zy9evJgZM2awfft2QkNDee+99yybvoXV5KVhY67B7Nld6SgdwpW1qYJqztDNlMpHW5OVjiSEEB2O2Wwmt9ggw/2uMWF4IOk5pfycWqR0FCGElWmwoNq3bx9hYWG4urpib29PREQE27dvr7dNXFwc48aN49577617zmAwcPjwYSIiIgCIiYm57n3WLvfnEwC4BIcqnKTjcA2bjM6rMw+7JfDdoRROp8mJSwghWlNeUSXVBjOBUlDVM2qgP3a2GnZKcwohxDW0DW2Qm5uLl5dX3WNvb29OnDhRb5snnngCgISEhLrnioqKcHR0RKu9/BFeXl7k5OQ0KVxSUlKD21z9mZZWc/wgepMd1cbq2/qclsxoKdaUUdNtDM4HPyLa8Thvf2zP4xO8UatUVpXxZiSjZUhGy2gLGYX1Sc0uAaCrFFT12NlqCR8UwLdHMoidEoq9XqYCCCEua7CgMplM9cZQm83mRo2pvtF2TR2LHRoaiq3tzVdoT0hIYPDgwU3aZ1Mk7VrJOZMX940bgUbdvHHkLZ3REqwv42DyDTmMPLKTA8VBFBn74qHNt7KM17O+7/F6ktEyJGPDqqurG3VRzBLi4uJYuXIltbW1zJ49m5kzZ9Z7PTk5mQULFlBeXs6QIUNYvHgxWq2WrKws5s2bR0FBAV27dmXZsmU4ODhw9uxZFi5cSFlZGXq9nldeeYXevXu3yrFYg/PZlwDo4uukcBLrM2F4IDsOXOD7o5lMHBGkdBwhhJVocMifr68veXn/WxcoLy8Pb2/vBnfs7u5OaWkpRqOxSe+zFsbKMuwNRVQ4dm52MSWaz33MTLSOrsx2O8Tqr5KorJE26kKI6zVmnu+8efNYuHAhO3bswGw2s379euDm83xfeuklYmNj2bJlC88//zwvvvhiqx+XklKzSnBz1MgdmBvo0dmVID9ndsiwPyHEVRosqEaOHMn+/fspLCyksrKSnTt3Eh4e3uCOdTodQ4YMYevWrQBs3ry5Ue+zFpWZZwCw8QtWOEnHpNY74BnxBJ6mfIYYj7HnxCWlIwkhrFBD83wzMzOpqqpi4MCBwP/m895qnu+0adMYPXo0AL169SI7O7uVj0pZqdkl+LhKMXUjKpWKCcMDSUkv5lymnJeEEJc1WFD5+PjwwgsvMGvWLKZMmcKkSZPo378/sbGxJCYm3vK9ixYtYv369URGRhIfH8/zzz9vseAtLS/lcoc5j24hCifpuBxCwrDvOYxIhxOcO3tRTl5CiOvcaJ7v1fN1r339ynzeW83zjYmJQaPRAPDOO+8wfvz41jgUq1BjMJKVVyYF1S3cPTgAnVYtzSmEEHUanEMFEBUVRVRUVL3nVq1add12S5curffY39+f1atX30Y85ZSln6bC6ES3rp2UjtKheUY8QWXqc0x3PMA/PuvC0rmjUcsQTCHELxqa53uz1xua52s2m3njjTc4fvw4H330UZNzNTR/zFobhmQV1mAyg7erzmozXkuJnCH+tnxzKJUB/tXYaBte0rMtfJeS0TIko2W0hYxXa1RB1RFpCi+QYfJiiJej0lE6NK2zB+5jHqbHjlUczI5nd3wg44cFKh1LCGElfH19iY+Pr3t87Xzda+cB5+fn4+3tXW+er0ajqfe+2tpaXnzxRXJycvjoo49wcmp6c4ZbNVVSumHIrRQdSgNy8XHVWW3Gqyn1Xdq45PPHlT9SqfFhxOAut9zWmv++r5CMliEZLUPJjM1tqNTwZZUOqLasCH1tCZWOAdKQwgo4D56AwTWAqY7xrP8ynrKKGqUjCSGsREPzfP39/bG1ta272rllyxbCw8NvOc/39ddfp6ysjH//+9/NKqbastTsEmx0Gtwd5XrrrYQGe9DJ04EdB2TYnxBCCqobqsy83CFKJw0prIJKpaYiNBK92sgE1T5Wb0tWOpIQwko0Zp7vsmXLeO2115g4cSIVFRXMmjULuPE838LCQtasWcP58+eZNm0a0dHRREdHK3mIrSo1+xKBvk4ytLoBKpWKiLBATp4vJO1iidJxhBAKk0tQN1Bw9iQmswrPbr2UjiJ+YXL0xG3UVO74/lNWxf9AyrBAund2VTqWEMIKNDTPNyQkhI0bN173vpvN8z158qTlQ7YRF7JLGdrHB5ClKhoydkgXVm9LZufBNJ6IDlU6jhBCQXKH6gbKM85w0ehCcJCP0lHEVVxHTkHr0ZkHHQ7xwcZDGE1mpSMJIUS7UVRaRXFZNUF+zkpHaRNcnWwZHurH7vh0agxGpeMIIRQkBdU1zGZzXUOKzt7SkMKaqDQ6vKOexllVQZ/CPew4kKp0JCGEaDdSsy4PXQvqJAVVY0UMD6S0oob9iR1rrTIhRH1SUF2j9lIeNsYKKpz80Wjk67E2ev+euAy7j1H60/ywbRdFpVVKRxJCiHbhwi9zgQJ9paBqrAE9vPBxt5c1qYTo4KRiuEZV5hkAbHy7K5xE3Iz73TPAyYv7dXv575ZjSscRQoh2Ie1iKa6Otrg43rjdu7ieWq1iwvBATqTkk5lXpnQcIYRCpKC6RtH5U9Sa1Xh166F0FHETap0tfpOfwVNTitPPX3EiJa/hNwkhhLil9JxSOvt0rDbxljB+WBc0apW0UBeiA5OC6hrlGafJNLoR3MVT6SjiFuyC+mE/YDx32SXz+YavMdTKhGAhhGgus9n8S0Elc4ebyt1Zz/BQX745lCbNKYTooKSguorZbEJTlEaG0ZNAX7lKZ+2875mN2c6F8TXfsGnXz0rHEUKINquwpIryqlq6yB2qZpkYFkRpRQ37pDmFEB2SFFRXqS26iNZUTYVjADqtRuk4ogFqW3v8Jz+Dn/YSJT9ukPHrQgjRTOk5pQB0louJzTKghxd+Hg5s35+qdBQhhAKkoLpK9cXzANj6dlU4iWgs++53YNP7LsbYJLH+0x2YzbI2lRBCNFXalYJK7lA1i1qtIiIskJ/OFZD2S7dEIUTHIQXVVYrTzmI0q/DuKh3+2hK/yMcx6p0ZVriVPYfPKx1HCCHanPScMpzsdbhKh79mGz+sC1qNNKcQoiOSguoqZRlnyTG6EBTgrnQU0QQavQP+0c/gpy0mddvHXCqrVjqSEEK0KVc6/KlUKqWjtFkujraM7NeJXfHpVEtzCiE6FCmorlaUTqbRXRY1bIMcewyGHqMYrTnBpg1fKx1HCCHaDLPZTNrFEhnuZwETRwZRXmlg77FMpaMIIVqRFFS/MFaUYlNziUs23jjY6ZSOI5ohcPIcam2c6JW+iSMnM5SOI4QQbcKlshpKKwzS4c8CQrt5EODtyNZ9MvxciI5ECqpf1OSmAqBy76JsENFsGr0D/lOexVdziZ8//zdV1bVKRxJCCKuXLg0pLEalUhE5siun04o5k16kdBwhRCuRguoXFVnnAHAMCFY4ibgdzj3voLb7XQwzH+fLTTuUjiOEEFbvSoe/LtIy3SLGDumM3kbDtn2pSkcRQrSSRhVUcXFxREZGMmHCBNasWXPd68nJycTExBAREcGCBQuorb18ZyAjI4OZM2cSHR3NI488Qmam9Y4pLk5LodhkR0AXP6WjiNvU/f5Yqmxc6XJmPafPyiKLQghxK+k5pdjrtbg765WO0i442Om4e3BnvjuSQWlFjdJxhBCtoMGCKicnh+XLl7N27Vo2b97MunXrSElJqbfNvHnzWLhwITt2XF4HaP369QD87W9/47777mPLli1MmDCB5cuXt8xRWIAhJ5WsWneC/KQhRVuntrHD//7n8FCX8dP6f2CoNSkdSQghrJZ0+LO8yJFB1NSa2HU4TekoQohW0GBBtW/fPsLCwnB1dcXe3p6IiAi2b99e93pmZiZVVVUMHDgQgJiYmLrXTSYTZWVlAFRWVqLXW+fVL7PRgLY8h2yzO508HZSOIyzArUd/KruPZYApia83fal0HCGEsFppOaXSkMLCunZyoXeQO1v3pWKSBeeFaPe0DW2Qm5uLl5dX3WNvb29OnDhx09e9vLzIyckB4LnnnmP69OmsXr0ag8HAunXrmhQuKSmpwW0SEhKatM8b0ZTk4Gw2UmrrybFjR297f9eyRMaW1i4zdhtC1fljdDq1nh3bHfH0cmmZYFdpl9+jAiSjZbSFjEJZJeU1FJdWS0OKFnDfnV1ZtiaBc9l2DFU6jBCiRTVYUJlMpnrDAMxmc73Ht3r9xRdf5E9/+hPjx49nx44dzJ07ly+++KLRwwpCQ0Oxtb35qu0JCQkMHjy4Ufu6ldITe8gDnDuHWGR/V7NUxpbUnjMWeLlRsGYB6mPbGfD719BqNS2Q7rL2/D22JsloGUpnrK6ubtRFMaEs6fDXckb298N1iy2HzpTxK6XDCCFaVIND/nx9fcnLy6t7nJeXh7e3901fz8/Px9vbm8LCQs6dO8f48eMBiIiIIC8vj6Ii62sjWpKeQo1Zg1dgoNJRhIV5dO1JeZ8ogo1n+WHjBqXjCCGEVblSUMmQP8vTaTVMCAvkdGYVFwvKlY4jhGhBDRZUI0eOZP/+/RQWFlJZWcnOnTsJDw+ve93f3x9bW9u6oSVbtmwhPDwcNzc3bG1tiY+PBy5fLXVwcMDd3b2FDqX5yjPPkWV0I6iTq9JRRAsYED2DXJvO+KRsJi3lnNJxhBDCaqTnlKK30eDpaqd0lHbp3hFBqFTw1Y+y0K8Q7VmDBZWPjw8vvPACs2bNYsqUKUyaNIn+/fsTGxtLYmIiAMuWLeO1115j4sSJVFRUMGvWLFQqFe+++y6vv/46UVFRvPnmm6xYsaLFD6ipzGYzFKWTWesmHf7aKbVGS/cZv8OMivQNb1FrMCgdSQghrEJ6TikBPk6o1dLhryV4utrRp7MdXx9Kk8XmhWjHGpxDBRAVFUVUVFS951atWlX355CQEDZu3Hjd+/r378+GDdY9zMpYWoC2tpIinTcujjefryXaNk//zqQOegi/Y//lwJpVjHr0aaUjCSEsJC4ujpUrV1JbW8vs2bOZOXNmvdeTk5NZsGAB5eXlDBkyhMWLF6PVasnKymLevHkUFBTQtWtXli1bhoPD/zq9btiwgYSEBJYuXdrah9Rq0nPLCA32UDpGuza8lyM/peWx50gG944IUjqOEKIFNGph3/as+uLl2/Aq984KJxEtbch9k0m174tvxm7OHY1XOo4QwgJuZ63ExYsXM2PGDLZv305oaCjvvfcecLmhxrJly/jLX/7S6sfTmiqra8kvrqSzt8yfakmdPW0IDnAh7odzl0fFCCHaHSmoclIBcA4IVjaIaBWDZr1AMY6UbH2X6vJSpeMIIW5Tc9dKNBgMHD58mIiIiHrPAxw+fBiTycS8efNa/4BaUWbe5XUiA7wdFU7SvqlUKibd2Y30nFJOnMlXOo4QogV0+ILqUsZ5CoyOdA7wanhj0ea5ebjB6FgczGUc++9bcrVQiDbuRmslXlkL8UavX1krsaioCEdHR7Rabb3nAUaNGsX8+fOtdjF6S8nIvVxQ+UtB1eLCB/nj7GBD3F5pjCREe9SoOVTtWU1uGtlGV/p1koYUHcWQu+7kq58S6F30HWd2x9Fz3GSlIwkhmqm5ayVeux3Q6DUSG6OhNbisYdHlwycuoVLBxbTT5Gdef+zWkLEx2kLOxBPHGBBkyw8/XeTr7w7i7mh9P7/awvcoGS1DMlqe9f0f3YrMxlo05blcNPXmXrlC16HcNftJDi4/Q8CBNZT07o9zpyClIwkhmsHX17dueQ5o/FqJ7u7ulJaWYjQa0Wg0173vdt1qYXqlF12+4uufDuPrYWL4sCHXvWYtGRvSFnJeyRjUvZJ9yV+TWmTPPXf1UzpWPW3pe7RmktEylMzY3EXpO/SQP/+qOeIAACAASURBVENhNmqzkWp7H3RajdJxRCtydLDFZ8pzVJm0nFvzOiZDtdKRhBDN0Ny1EnU6HUOGDGHr1q0AbN68ud77OoLM3DKZP9WKPFzsGD3In68PXaCsUpbvEKI96dAFVU1+OgBaT+nw1xGFhnbnfPA0nGty+XnDe0rHEUI0Q3PXSgRYtGgR69evJzIykvj4eJ5//nklD6VVGU1mMvPKCJAOf60qOjyYymojOw9cUDqKEMKCOvSQv8qLFzCZVbj4BykdRSjkvgej+HxZEkPO7yUnYSA+g8coHUkI0UTNXSvR39+f1atX33S/MTExxMTEWC6oFckrqsBQa5I7VK2se4Ar/YI9idt7jsnh3dBqOvR1bSHajQ79f3Jp5nnyTE509nNXOopQiE6rYdgjT3O+1pviHe9Tk5+pdCQhhGhxVzr8SUHV+qbcHUx+cSX7TmQpHUUIYSEduqAy5Kdz0ehKF18Z8tCRBfm7U3tnLNVGNWc+fk3mUwkh2r26luleUlC1tiEhPvh7OfD5d2dl6Q4h2okOW1CZamvQlueRY3Klk5xQOrwJ4wZxyGMSduXZpG7+h9JxhBCiRWXkluJkb4OL4407EYqWo1ariA4PJiW9mJPnC5WOI4SwgA5bUBkKslBhptrBB522w34N4hcqlYppsx7gB+NAOP09hUd3KR1JCCFaTIZ0+FPUmCGdcbK34fNvU5SOIoSwgA5bSdTkpQGg8+yicBJhLVwcbek37QlOG3wp2PZPqi+eVzqSEEK0CGmZriy9jZZJo7py8KeLpF0sUTqOEOI2ddiCqjLnAkazCjd/KajE/9zR24/CgbMpNdpw4ZPXMFaWKR1JCCEsqrSihuKyammZrrD77uyKjU7DZ3vkLpUQbV2HLajKMlPJNboQ4OemdBRhZR6MGsIex0lQXkT6xrcxm03/v707j4+qvPv//5o9+z6TnRACIUCAQAIBlAAKhC2CLBVQ0Wpd+msFaaWieKMoivKl4q1Vete7elcKFkQEUYiobLKoEEAI+07WmSyE7Mlk5vz+QNOGLQFCTpbP8/HgYc4yJ+8zZnLlc851rkvtSEII0WiyfhnhL1DuUKnJ28NEcr8Itu7NJO9ChdpxhBC3oM0WVPb8DHIc3jLCn7iCXqflwYdTWG9PxHn+Jwq2faJ2JCGEaDSZthJAhkxvDsYlRQGwZpvcpRKiJWuTBZWzuhJDRQFWpy8hAdKgiCtZfN3oP3EqP1Z14OL2lZQd3612JCGEaBSZtlL0Og2Bvm5qR2nzLH5uJPUKZeP35yguq1Y7jhDiJrXJgsqenwlAtUeQjPAnrimxewjlvaaSUeNPzmeLqf7550YIIVqyTFspwQEe6HTS/jUHE4Z0orLawZc7ZCAkIVqqNvnbtHaEP7MMSCGub9o9PdnqM45yu4bMfy3AWVmmdiQhhLglMmR68xIR7EXfrkGs++40lVU1ascRQtyEBhVU69atY9SoUQwfPpxly5Zdsf3IkSOMHz+e5ORk5syZQ03NpV8INpuNxx9/nHHjxjF58mQyM5vHFf4K63nsiha/0HC1o4hmTq/T8vuHh7Ci5m4cF23kfPYWitOhdiwhhLgpNQ4nuQVlUlA1M5Pu7kRJeTUbdp1VO4oQ4ibUW1BZrVYWL17M8uXLWbNmDStWrODkyboPT86aNYu5c+fy1VdfoSgKK1euBOBPf/oTQ4YMYc2aNYwdO5ZFixbdnrO4QSXZZ7A6vGkX7K12FNEC+Hu78qupKXxWnkDV6b0Ubr7yooIQQrQEOfllOJyKFFTNTEx7P+I6mVm95SSV1XKXSoiWpt6CaufOnfTr1w8fHx/c3NxITk4mNTW1dntWVhaVlZXExcUBMH78eFJTUyksLOTo0aNMnjwZgAkTJvD000/fptO4MY6CTHIdPrQLlBH+RMP0jDYTMXgs2yujufj9Wkp+2qR2JCGEuGGZvwyZLnNQNTuTh3emqKSKjd+fUzuKEOIG1VtQ2Ww2zGZz7bLFYsFqtV5zu9lsxmq1kpGRQUhICK+//joTJkxg+vTpGAyGRo5/45zVFegri7ApPoSY5QqdaLhJd3cmo30Kx+3B2Nb/D5UZR9WOJIQQNyQr71JBFSrtX7PTrYM/sVH+fLr5JNV26VouREuir28Hp9OJRqOpXVYUpc7ytbbX1NRw+PBhnnrqKZ577jk++eQTZs+ezdKlSxscLj09vd590tLSGnw8AN3FHLyAMoMvP+3fd0OvvVk3mlENkrFhBnczsDTzLh6p+Rznx69S2v9hnG4+tdubQ8b6SMbGIRlFS5RlK8XX04S7q/oXOMWVJg/rzAt/3cnXP55n9B2RascRQjRQvQVVUFAQe/bsqV3Oy8vDYrHU2Z6Xl1e7nJ+fj8ViwWw24+7uzpAhQwAYM2YM8+fPv6FwsbGxmEyma25PS0sjPj7+ho5ZcnAreYBnaIcbfu3NuJmMTU0y3ph2kTEseLuS32u/wP/Q54Q+/Bo6F/dmlfFaJGPjkIz1q6qqatBFMdG0Mm0lhMrzU81Wj44BdGnvx6pNJxieGCFTuwjRQtT7SR0wYAC7du2isLCQiooKNm7cSFJSUu320NBQTCZT7ZXQtWvXkpSURLt27QgKCmLr1q0AbN68mW7dut2m02i4ClsGDkWDb4iM8CduTnigJ9OmDOH94kFUF2RjXbUQxWFXO5YQQlyXoig/D5kuz081VxqNhsnDOpNfVME3u8+rHUcI0UD1FlSBgYHMnDmTadOmMW7cOMaMGUOPHj147LHHOHjwIACLFi1iwYIFjBgxgvLycqZNmwbAO++8w//+7/8yZswYPvroI1577bXbezYNUJpznnynJ2FBvmpHES1Yv9hgEocOZnlpfyrPpZO3/n9AUdSOJYQQ11RcVk1phV2en2rmenU206W9Hyu+PibPUgnRQtTb5Q8gJSWFlJSUOuvef//92q9jYmJYtWrVFa/r0KHDDT0z1RTsBZlYHd70DJQGRdya+4ZGszCnmNTjJYw4sBmXCgckJKgdSwghrurfI/xJ+9ecaTQaHhgZw5wlO1m/8yzjBkWpHUkIUY821TlXcdSgK8vD5vCWEf7ELdNoNMyY3IvjfknstUfhemKbDKcuhGi2fhnhTwqq5q9HRzM9OwWwatNxKqpkXiohmrs2VVDZL+SiVZxUuJoxGXRqxxGtgItRzwuP9ONLBnHSGULel0soP7lX7VhCCHGFTFspBr0Ws6+b2lFEAzw4sgsXS6v5/LtTakcRQtSjbRVUBVkA6PxCVU4iWpMAH1eee2QAH5QMJk/jj3X1IiqzTqgdSwgh6siylRIc4I5Oq6l/Z6G6zhF+JHYL4rPNJyktr1Y7jhDiOtpUQVWVlwmAZ3A7lZOI1ia6nS9jBgTyduFgSpwu5K54jeqCbLVjCdEmrFu3jlGjRjF8+HCWLVt2xfYjR44wfvx4kpOTmTNnDjU1l7pQZWdnc//99zNixAh++9vfUlZWBkBxcTGPP/44I0eO5P77768zNUhLlpVXIt39Wpj7R8RQXlXD6i0n1Y4ihLiONlVQFWefpcjpRkhwgNpRRCvUJdyVSWMSeKtgCJV2B7nL51FTnK92LCFaNavVyuLFi1m+fDlr1qxhxYoVnDxZ94/PWbNmMXfuXL766isURWHlypUAzJs3j6lTp5KamkpsbCzvvfceAG+99RYJCQls2LCBSZMm8eqrrzb5eTU2e42TnIJyGeGvhYkM8WZgXChrt52m4GKF2nGEENfQpgqqqrwsrA5vwgNlDg5xe4xNiiKhXw/+u2AwVWWl5Cx/GUd5sdqxhGi1du7cSb9+/fDx8cHNzY3k5GRSU1Nrt2dlZVFZWUlcXBwA48ePJzU1Fbvdzu7du0lOTq6zHmDLli21I9uOGTOGbdu2Ybe37LnmcgvKcDoVuUPVAj04sgtOp8Ky1KNqRxFCXEODhk1vDRRFQVuSi9XRnoFSUInbRKPR8MS47iy4WMm7x2t4StlE7r/mE3z/S2hN8iC4EI3NZrNhNptrly0WCwcOHLjmdrPZjNVq5cKFC3h4eKDX6+usv/w1er0eDw8PCgsLCQwMbHCu9PT0625PS0tr8LEaw9HMS3c3SgqySEtrWBfGps54s1pCzlvN2KeTG1//eJ4o/0qCfI2NlKqutvA+NgXJ2DhaQsb/1GYKKkdJITpHFSWGADxcDWrHEa2YTqflmQfi+a+/VvGBtYZHlM3krlxA0OQX0BpMascTolVxOp1oNP8eZEFRlDrL19p++X7AFcv/+Rqt9sY6dMTGxmIyXf3znpaWRnx8/A0d71aduXgCKGBoUgLuDWgD1ch4M1pCzsbIGN2lmoOvfcOPp2He441/vm3lfbzdJGPjUDNjVVVVvRfErqbNdPmrzr80IIXGJ1jlJKItcDHq+a9H+1Hg2Zl/VQ2iMuMI1k9ex1kjIzUJ0ZiCgoLqDBqRl5eHxWK55vb8/HwsFgt+fn6UlJTgcDiueJ3FYiE//9LzjzU1NZSVleHj49MUp3PbZNlK8fE0NaiYEs2Pp5uR+4ZFs/eYjb3HbGrHEUJcps0VVK6B4SonEW2Fl7uReY/357i2I2tqBlFx5gC2TxehOFr2sxhCNCcDBgxg165dFBYWUlFRwcaNG0lKSqrdHhoaislkqu0+snbtWpKSkjAYDCQkJLB+/XoA1qxZU/u6QYMGsWbNGgDWr19PQkICBkPLLkSy8krl+akWbvQdkQT6ufHhukM4nIracYQQ/6HNFFSlOecodxoIDJE7VKLpBPq58fLjA9hdHUUqSZSfTMP62WIUR43a0YRoFQIDA5k5cybTpk1j3LhxjBkzhh49evDYY49x8OBBABYtWsSCBQsYMWIE5eXlTJs2DYAXX3yRlStXMmrUKPbs2cPTTz8NwIwZM9i/fz+jR49m+fLlzJ07V7XzayyZthIZ4a+FM+h1PDSqK2dzivn6h3NqxxFC/Ic28wxVuTUDq9Ob8EAvtaOINiYi2IuXHuvHC391YvJ2MuTYdqyfvUngvTPR6Fr2VW8hmoOUlJTaUfl+8f7779d+HRMTw6pVq654XWhoKEuXLr1ivY+PD3/9618bP6hKLpZWUVJulztUrcCdcSF8udOfj9Yf4Y6eIXi63Z4BKoQQN6bN3KGiKBurw5uwQGlQRNPrHOHHC79O5IvCjmw3JlF+7Aesq9+U7n9CiNsuK68UgDCLjHDb0mk0Gp64tztlFdUyjLoQzUibKKgcFaXo7aVc0Pji5+WidhzRRvWMNvPstAQ+tUWy3WUw5cd/xLr6z1JUCSFuq0zbpYJKuvy1DpEh3owcEMmGnWc4k31R7ThCCNpIQWUvyALA6RV8zWFxhWgK/WKDeeb+eD7NacdOtyGUH99N7icLcdqr1I4mhGilsmyl6HVaLH4yF15rcf+IGNxdjfzPZwdRFBmgQgi1tamCymQOUzmJEDAwLpSZU3qzMiucnR7DqDi1j9wVr+GsrlA7mhCiFcqwlRBidkenlQuKrYWnm5Fpo7pw6HQBW/dmqh1HiDavTRRUZdYMahQtfqFSUInmYXB8ONN/1YsV54PZ5jGCyvOHyVn+Co7KMrWjCSFamUxrKeHy/FSrMywxgo7hPvz980OUlMsch0KoqU0UVKU558l3ehIe6K12FCFqDe3bjum/imN1hplv3UdTlXOSnH++SE1pkdrRhBCtRLXdgbWwTAZkaoV0Wg1PTYqjuLyaD9cdUjuOEG1amyioagqzsTm8CA+UK3SieRmWGMHTk3vxRYYvG9zGYi/IJvujOdgv5KodTQjRCmTnl+FUkDtUrVSHUG/uHRTF1z+e5+DJfLXjCNFmNaigWrduHaNGjWL48OEsW7bsiu1Hjhxh/PjxJCcnM2fOHGpq6k5aevjwYWJjYxsn8Q1SnA70FQXkO70JlAdyRTN0V0I7Zk6NZ2OGB58ax+GoKCX7H3Oosp5VO5oQooXLsJYAyAXFVmzy8M4E+bvxl0/2U213qB1HiDap3oLKarWyePFili9fzpo1a1ixYgUnT56ss8+sWbOYO3cuX331FYqisHLlytptFRUVvPLKK9jt6gwNXVNkRas4qHa3oNO1iRtyogUa3DuMPz3Yhx05LnykjEXRaMlZ+l9UnD2odjQhRAuWaS1Bo4FQmdS31XIx6vndxJ5k55ex8pvjascRok2qt8LYuXMn/fr1w8fHBzc3N5KTk0lNTa3dnpWVRWVlJXFxcQCMHz++zvbXX3+dhx566DZEb5jq/Esj/Bn8Q1XLIERD3NEzhBceSeRAvpF3y0eDmy85H8+nNP07taMJIVqoDFspFl83TAad2lHEbRQXbeGuhHBWbTrByUx5DleIplZvQWWz2TCbzbXLFosFq9V6ze1ms7l2+7fffktlZSUjRoxozMw3pDLv0nCinsHhqmUQoqHiYwJ5+fH+nC81sLBwGJrAKGxr3+LCjtUy14gQ4oZlWEuku18b8djYWLw9TLy5fK90/RNtgqIo5BaUsTktg/c+/Ynpf97M/XM3UHCx6aeh0de3g9PprDMZrqIodZavtT0vL48lS5bwf//3fzcdLj09vd590tLSrrtdc/gAOqcLlVXl9e57u6j1fW+EZGwcjZXxgcF+LNuSz/Mn+/JMuAa2LCP35CHKuyaD9tauNLel9/F2koyiuXM4FbLySomLNte/s2jxPNyMzLivFy++v4t/ph7lkZRuakcSolE5nQrncotJP1XA4TMFHD5TSGFxJQCuJj2dI3wZ1CsMHw9Tk2ert6AKCgpiz549tct5eXlYLJY62/Py8mqX8/PzsVgsbNmyhaKiIu6///7abWPHjmXZsmV4eDSsL3dsbCwm07XflLS0NOLj4697jCM//ItMhxdJ/XrQIbTph01vSEa1ScbG0ZgZ44GEXmW8+LddLDjXj5fiI3A7/hXeOjuBE2ahc725K85t7X28XSRj/aqqqhp0UUzcPrbCcuw1TrlD1Yb0jrEwckB71mw9Sd+ugcRGBagdSYib5nAqnMm6yMFT+Rw8lc/hM4WUVVwakyHAx5XYKH+6RvrTNdKPdkFeqk5eXm9BNWDAAN555x0KCwtxdXVl48aNvPLKK7XbQ0NDMZlMtY332rVrSUpKYtKkSUyaNKl2v86dO7N27drbcxbXoS2xYnMGM9Ds3uTfW4hbERzgzsKnBjLv798z50eFZwdMIejYJ2R9OJug+57HKM8FCiGuI8P28wh/MmR6m/LImG7sP5bH4n/t450/DsbNxaB2JCEa5Jc7ULuOlvDl/u85dLqA8spLI4eHBLhzR48QunXwJ7aDP5ZmNnJ3vQVVYGAgM2fOZNq0adjtdiZOnEiPHj147LHHmD59Ot27d2fRokW88MILlJaW0q1bN6ZNm9YU2evlqCjBUFNGmSkAF2O9pypEs+PjaeK1397B6x/tZsF2G7/u+xC9sz8h+8PZWMbNxK1jb7UjCiGaqczaIdNlhL+2xMWkZ+aU3sx+9zuWrD7AH6b0rvNohhDNibWwnP3H8/jpxKV/xWXVAIQE1DAwLpTuUQHERvnj7+2qctLra1CVkZKSQkpKSp1177//fu3XMTExrFq16rrHOHbs2E3EuzX2gmwAtN7BTf69hWgsriY9cx9J5H/WHOTDnWfJ6DKVe50byF3xGr6Dp+Iz4F5pLIUQV8iwluLjacLDzah2FNHEukT6MSU5hmWpR+kRFcCwxAi1IwkBQHmlnYMn89l3PI+9x2zk5JcB4OdlIj7GQs9OZqjI4e6kRJWT3phWfdum6uch090CZYQ/0bLpdFp+O74HoWYP/v55Opmho5jeaR8XtiyjOvc05pTfoTU276s3QoimlWErke5+bdiku6NJP5XPXz87SHSELxFBXmpHEm2QoiiczSkm7aiNvUdtHD5TgMOpYDLq6B4VwJg7IomLNhMe6Fl7cTgtLa+eozY/rbqguph1lhpFi39omNpRhLhlGo2GsUlRBPm58eflabxQHMucvmGU7VtNdX4GgeOfwWiWiwdCiEt/xGRaS0jqLe1fW6XTavjj1Himv7mFNz7azZszBuFiatV/9olmoqKqhv3H89hzxMqeI9bakfgiQ7wYNyiK3jEWurT3w6BvPfPjtepPVrk1k0KnJ2FBPmpHEaLRJMYG8/+eSmL+hz/w7GYPnrnrScKOLiPrw2cxj/otHrED1Y4ohFDZhZIqyipr5A5VG+fr5cIzU+P5r7/t5L1Pf2KmPE8lbpPcgjJ2H7ay+3AuB08VUONw4uaip1e0hfgYC71jLM3+Oahb0aoLKmdRDjaHF7EyZKxoZSKCvfjzjEG88dFuXv86nwl9H2Vo5Xpsa9+iIuMw/kMfRmto+nkYhBDNQ4YMSCF+1jPazJThMSz/6ihRYT6MTYpSO5JoBZxOhZOZRXyfnsOPh3I5l3vpd06YxYOUgR3o0yWQLpF+6HValZM2jVZbUClOB8aKfC7qYvFylwdyRevj5W7k5cf7839fHubTrac40m4oT/WKomTvl1RlHsVy7x8xBkh3HyHaokxbKYDMQSUAuG9oNGeyL/LB5+m0C/SkV2dL/S8S4jL2GicHT+bzfXoOPxzKobC4Cq1WQ7dIfx69J4K+3QIJCWibF3FabUFVU2RFixOHR5DaUYS4bXQ6LY/eE0vnCF/eXrGP2YXBzL7792jTPiLrgz/hP/wRPHveLV08hGhjMq0luJr0+Hm5qB1FNANarYaZU3oz6+1tLFy6hz8/ndRm//AVN6aiqoa9R23sOpjD7iO5lFfW4GLUER8TSGJsEAldAvGUkURbb0FV/fMIf8YAmfxUtH539gwlIsiLBf/4kec/L+aBQb/lzotfkv/lEspP7sU86kl0bjLCk2h9srOzmTVrFgUFBURGRrJo0SLc3etO5F5dXc2cOXNIT0/HxcWFRYsWERUVhaIoLFy4kM2bN6PVannllVeIj4+vfZ3VamXChAls3769qU/rlmXYSggP9JCLKaKWq0nPC48k8oe3tjL/gx9Y+FQSHq4y6a+4UlmFnR8P57Ljp2z2HbNRXePEy93IHT1C6Nc9mLhOZoyG1jOgRGNotR0bi3POA+ATKnMviLYhPNCTP88YxJD4cJZuyeEvF+/GZcBkyk+kkfm3mZSf2qd2RCEa3bx585g6dSqpqanExsby3nvvXbHP0qVLcXV1ZcOGDTz//PM899xzAHz11VecOnWK9evX8+677/Lcc89RU1MDwNatW5k2bRp5eS1v+F64NAdVmAxIIS4T5O/O7If6kJ1Xxqsf/kC13aF2JNFMlJZX882P55n3v9/zwIsbeHP5Xk5mFjE8MYLXfnsHH72YzPT7etG3a5AUU1fReguq3CxKnC6EhAaqHUWIJuNq0jNzSm9mTunNicxintnkQcHAZ9C6eZL7r/m4HdqAs6pC7ZhCNAq73c7u3btJTk4GYPz48aSmpl6x35YtW7jnnnsA6NOnD4WFhWRnZ7N161ZGjRqFVqslMjKS4OBg9u27dOFh1apVvPPOO013Mo2opLyawuJK2snzU+IqenQ08/TkXqSfKuDN5XtxOBW1IwmV/FJEvfT+Lh54MZX/XrGP87nFjLmzA/9v+kA+eGE4T4zvQfeOAejayOASN6vVdvnL8o0ntUzPMxbpIyzanrsSwolu58OiZWm8/Fk2I/o8wMSIgyh7viDz/ZmYx/wO1/bd1Y4pxC25cOECHh4e6PWXmjKz2YzVar1iP5vNhtlsrl02m83k5uZis9mwWCxXrAdabDEFcDanGIDIEG+Vk4jmanB8OBdKqvhg3SF81xwkvp0UVW1Fpd3Jpj0ZfLc/i/3HbdQ4FCx+boxNiuKOniF0CveRrsI3odUWVKfKvTitaUeAT+sd816I6wmzePL/nkpi+VdH+XTzCX7yC2di58l0ydtKzrKX8Ow1HP+7HkDr4l7/wYRQ2YYNG1iwYEGddREREVc0/Ff7Q0BRlDrrFUVBq9XidDqvur4xpKenX3d7Wlpao3yfq/nh2KUR/orzz5KWlnHTx7mdGRtTS8jZHDO284T+MR58seMMZcVeaDTNL+PlmuP7eLnmmLG6xsnxrErSz5VzIrsShzMbbzcdfaPd6dbOjRA/AxpNJSV5p9nbTHo5N8f38XpabUHVJdIPV5MerVaqbNF2GfRaHhrdlfgYC4s/3stfvjcyfuCjjOqwn5K09ZSf2ENA8m9wj0lUO6oQ1zVy5EhGjhxZZ53dbicxMRGHw4FOpyMvL6/OHadfBAYGYrPZaNeuHQD5+flYLBaCgoKw2Wy1+/2yvjHExsZiMl19Lri0tLQ6g180tp2n9uPlXs6gO/rc9JXm252xsbSEnM05Y69eCv+9Yh+b9mQQFhbKr4ZGqx3pmprz+/iL5pTRXuNk3zEbW/dl8uMhK5XVDvy8TCR09GBici86R/g22ztRar6PVVVV9V4Qu5pWW1Dd2TOUO3vKCH9CAMRGBfDOM0NY+OFWPt12nh8s7ZiZPBvj3mVYP12IW+dEAoY/it7LX+2oQjSYwWAgISGB9evXk5KSwpo1a0hKSrpiv0GDBrF27VoSEhLYs2cPJpOJkJAQkpKS+PTTTxkzZgyZmZmcPXuW7t1bflfYM9kXiQzxarZ/LInmQ6vVMP2+XuTnF7B0wxE0Gph0d/MtqsT1OZwKh07ns3VvFjsPZFNaYcfTzcCg3mEM6hVG1w7+7N+3l5j2fmpHbXVabUElhKjLzcVASl9fxt7Vg7dX7ueZjzO5545p3NP5JGW7PiXjr9PxHTgJ775j0OjkV4NoGV588UVmz57NkiVLCA4O5s033wTg448/xmazMWPGDB588EHmzp3L6NGjMRqNLFy4EIARI0Zw4MCB2gErXn31VVxcWva8TQ6nwrncEkb2b692FNFC6LQaxvXzxdfXj4/WHwGkqGpJFEXhREYR2/Zl8d3+TAqLq3A16UiMDWZQrzDios3oZUCJ207+ahKijenV2cK7s4bw0fojfL7jDDu8vfj9iDmEnv6cwk1LDpebDAAAIABJREFUKTmwmYARj+EaEat2VCHqFRoaytKlS69YP2XKlNqvTSYTb7zxxhX7aDQann32WZ599tlrHv/YsWONE7SJ5BaUUW130D5Y5p0TDXdp4t9eAHy0/ggl5XYeHt1VHptoxjJtJWzbl8XWvZlk55eh12lJ6GIhqVcYfboG4mKUP/GbkrzbQrRBbi4Gnhzfg0G9wnjnk/289K9T9O8+lIdHJlGz85/k/PNF3GP64Xf3NAw+MvWAEC3F2exLI/y1D5GCStwYnU7LzKm98XAz8NmWk1woqWTGfb3k7kYzUnCxgu/2XyqiTmZeRKOB7lEBTLirEwO6B+PhZlQ7YpslBZUQbViXSD/++w+D+WzLSVZ8c5y9x2DyXU8x2HiIkh/WUH4iDe/EFHwG3IvW5KZ2XCFEPc5kX0Sr1cgcVOKm6LQanri3O35eLizdcITi0mqenZaAm4tB7WhtVmmFnV0HstmyN5ODp/JRFIgK8+bRe7oxMC4Uf28Zzbo5kIJKiDbOoNfyq6HRDO4dxvtrD/KP1JN8Y/bjN8P+i/CMryjauZri/d/gO/A+vHoNleerhGjGzuYUE2r2wGjQqR1FtFAajYZfDY3G19PEX1b9xDNvb2POrxMJNcu8nk2lyu5gz2ErW/dlsvuwlRqHk+AAd+4b2plBvUMJs8gFk+ZG/jISQgBg8XNjzq8T2XPEyv+uTWfe8uPERffl0ZTBGH9aTcFX71O8+0t8B0/FPSYRjUa6gQjR3JzJKSamna/aMUQrMCwxgkB/N974aA9/fGsrf7w/nj5dg9SO1Wo5HE72n8hj274sdh3MoaKqBl9PE6PuaM+gXmEy4W4zJwWVEKKOhC6BxEWbWb/jDMs3HmPGiTyG9rmXSaNHYP9hBbbVizAGdcBv0BRco3rJL3ghmomyCju2wnJG9ItQO4poJXp0NLP46UG8+n8/8soHPzB5WGfuGxqNTp6rahROp8LhMwVs25fFjgPZFJdV4+6i586eIQzqFUZsxwB0MjBIi9CggmrdunUsWbKEmpoaHnroIe6///46248cOcKcOXMoKysjISGBefPmodfrSUtLY8GCBdjtdnx8fHjttdcIDZW5oYRo7vQ6LfckRTGodxgrvznO+p1n2LJPy9iBjzEqwUr596vIXfEqprAYfAf+CtfIHlJYCaGyszk/D0ghI/yJRmTxc2PhUwN5b9VPfLzxGHuP2fjj1HiCA9zVjtYiKYrCsfMX2L4/m+0/ZVFwsRKjQUdityAGxoWS0MWCQS9ddluaegsqq9XK4sWLWb16NUajkcmTJ5OYmEjHjh1r95k1axbz588nLi6O559/npUrVzJ16lRmzZrFe++9R0xMDKtWrWL+/PksWbLktp6QEKLxeHuYeGxcd1IGdmDphiN8sukUG1wNTBj0FIO9zlH2w2fkfvwyptDO+A6chGuHOCmshFDJLwVVZIi3yklEa2My6Jg5pTfxMRbe+/QAM97czG/GdmdY33byO78BfpkravtP2ez4KQvbhQr0Oi3xMRZ+PSaUvt2CcDVJp7GWrN7/ezt37qRfv374+PgAkJycTGpqKr///e8ByMrKorKykri4OADGjx/P22+/zcSJE5kxYwYxMTEAdO7cmX/+85+36zyEELdRkL87sx5I4N7BHVmWepR/pJ5gjYeRiYP+wED3M5T+uIbcf83HGBSFz4B7ce/cF41WrrAJ0ZTO5hTj4WrA37tlT04smq+kXmF0ae/PW//ayzsr97N1byZPju9BuIwqeQWnU+H4+QvsPJjDjgPZ2ArL0Wk1xEWbmZocQ2JsMB6uMnpia1FvQWWz2TCbzbXLFouFAwcOXHO72WzGarViNBoZO3YsAE6nk7/85S8MHTr0hsKlp6fXu09aWtoNHVMNkrFxSMbGcasZx/Qy0DPMzKYDxfz9y2N8bNIyoPMkkkLO4nH+B6pXL8Lh5kdlZD+qQ2LhJkYFbAvvY1NoCRlF4zmbfZH2IV5yx0DcVmZfV155YgBf/XCOf3x5mOl/3sy9gzvyq7ujcWnjd1kcToWfTuTx/cEcdqXnUHCxEr1OQ89OZqYM60y/2CCZK6qVqvcn3+l01vnlrChKneX6tldXVzN79mxqamp44oknbihcbGwsJpPpmtvT0tKIj4+/oWM2NcnYOCRj42isjPHAuBFw+EwBK745zjcHbHzvGsLoAU8zPCif6r3r0B1aj+eZ7XjFj8A7fgQ694Z1Q2pL7+PtpHbGqqqqBl0UE43D6VQ4l1vM3X3aqR1FtAFarYaR/dvTPzaYD784xCffnuCbH89z39Bohvdrj0HfdgatKK+0s+9YHj8cymHXwWwqq7Mw6rX0jrHw0OgQ+nQNkjtRbUC9BVVQUBB79uypXc7Ly8NisdTZnpeXV7ucn59fu72srIzf/va3+Pj4sGTJEgwG+YESojXpGunPvMf6c/z8BT759jgrN53kM52WuxMeIKWPHcPRryn6biUXd36Ge7c78E4YhSk4Su3YQrQ61sJyKqoctA+W56dE0/HxNDFzSm9G9GvPP9Yf5q+fHWT11lNMHhrN4PiwVjm4gqIo5OSXseeold2HraSfyqfGoeDpZqBzqCujB8XSK9rc5u/WtTX1/t8eMGAA77zzDoWFhbi6urJx40ZeeeWV2u2hoaGYTKbaq6Fr164lKSkJuDRYRUREBPPmzUOrbTtXK4Roa6Lb+TLn14lk2kpYs/UUX+/OIPUHJwld7uLe5DEE5X1P6cGtlB7Ygim0M17xybh36Y9WL10fhGgMZ7IvAhAZIiP8iabXJdKPBf/fHew7nsfS9Yd5e+V+PtpwhFEDIhnZvz0+ntfubdQSlFXYOXgqn/3H80g7aiW3oByAMIsHKQOj6Ns1kC7t/di/fx/x3YNVTivUUG9BFRgYyMyZM5k2bRp2u52JEyfSo0cPHnvsMaZPn0737t1ZtGgRL7zwAqWlpXTr1o1p06Zx+PBhvv32Wzp27Mi9994LXHr+6v3337/tJyWEUEeYxZPfT4rj/uQYNuw6y/qdZ3j+sJWIoI6M6Xcn8fqTVP70NXmfv03B1x/g2X0wnr2GYQwIUzu6EC3asXMX0Ou0MmS6UI1Go6F3Zwu9os38dCKPNVtPsfyro3zy7XH6dgvirvhwesdY0LeAOazKK+0cPXuB9NP5HDiZz4nzF3AqYDLq6NnRzLhBHYmPsRDkL0PHi0sadD8yJSWFlJSUOuv+szD6ZVj0/9S1a1eOHTvWCBGFEC2Nr5cLU5NjmHhXJ7bty+KLHad5d+0JXE06Bvd6lBF9KnE9v4OLe1K5+OMXmEI749lzCB5d71A7uhCqW7/zDB3DfIhu59vg1xw6U0CncB+MhtbXxUq0LBqNhrhoC3HRFjKsJazfcYZt+7PY8VM23h5G+sUG06dLID07NY9ucYqiYC0s5+i5Cxw7V8jRcxc4nVmEUwGdVkPHcB8mDY0mrpOZzhF+ber5MNFw6v8kCyFaLaNBx9C+7bi7TzgnMor4cscZvtmTwYbvnXQMi2dk/2HE6U5RdXgL+ev/SsHGD3Azd6LcW4Nrh54y9Lpok9ZuPUVkqDezp/Vp0P6V1TWcyixibJI8nyial/BAT54Y34NHx8ay96iNzWkZbNuXyVffn8Og19Ktgz9d2/vRub0fndv54n6bB2+orK4h01ZKprWE09nFnM4q4nTWRUrK7cClO1DR4b5MGhpNbAd/Okf4yfxQokHkp0QIcdtpNBqi2/kS3c6X34yNZUtaJht/OMc7685g1OvpF/sAw4Y4CCnajyP9O3JXvIrO3Rv3rnfg0fVOTKHRMhS0aDM6hHpzIqOowfufOF9EjUOhWwf/25hKiJun12np2y2Ivt2CsNc4OXy6gN1HrPx0Io+Pvz6GooBGA2ZfN8ItHoQHehIc4I6/lwt+3i74erpQaXficCrotFe2BQ6nQmVVDRVVNRSVVnGxtIqikiryL1ZgLSjHWlhObmE5eRfKUZR/Z2of7MmAHiFEhXrTOcKPiCBPdC2gS6JofqSgEkI0KU83IykDOzDmzkhOZBTx7e7zbNuXxbb9dnw92xMT3IGJXbW45aZRsvdrinevR+9txr3LANxj+mEK6STFlWjVOoX7sP2nbC6WVuHtUf/D/IfPFKDRQJf2fk2QTohbY9Br6Rltpmf0pTlMyyvtHD9/gWPnLnA+t4QMWwkHT+ZTXeO88sWffI7JqEOn1dQWRg6nQrXdcc3v5+NpItDPjS4Rfgzr245wiydhgR6Emj1axPNcomWQgkoIoYrL71rtOWJlc1omPx7KYddxCPLvzeDuw0j0ysWQs4+LP37Bxe/XovMKwL1zIu6d++IS3kW6BYpWp2O4DwCnMi/SO8ZSz95w6HQBEUFeMmGoaJHcXAy1z1z9wuFUKCqppLC4ksKLlVwoqeLEqbMEmIMor6rB+XM1pUGDVqvB1aTH1aTD1aTHy92Ij4cLPp4mfL1MuBjlT11x+8lPmRBCdQa9jv7dQ+jfPYQdu3ZToQtk275MVm7L5F9OhUC/viR1TaavVy7eBQcp2buR4t1fonX1wK1jPG6d+uAW2QOti4y4JFq+qNBLBdWJzAv1FlQOh5Oj5woZEh/eFNGEaBI6rQZ/b1f8vV3h5x9ts7GA+PgYdYMJcQ1SUAkhmhUXo5Y74tsxtG87isuq+SE9h+0Hslm9M5tPnAo+Hr3oFzOE/n6FBJcfp/xkGqUHt4JWh0t4DG5RvXGL6oXB3E66BooWyd3VQKjZnRPn63+O6kxOMRVVDrpGyvNTQgihFimohBDNlpe7kWGJEQxLjKCswk7aUSs/pOeyLd1KamUNel0U3TskcGfHSjppz+PMSadw01IKNy1F5+GLa2RPXCN74Nq+O3pPeb5EtBydwn05eCq/3v0Ony4AkAEphBBCRVJQCSFaBHdXA0m9wkjqFYa9xsmRswXsPmxlzxEr75woA/wJ8E6mf5QLvT3zCKw8Q/nJPZQe3AKAISAM14hYXCK64RLeFb2Hj6rnI8T1dAz3YcveTAqLK/HzcrnmfofPFGLxdSXAx7UJ0wkhhPhPUlAJIVocg15Lj45menQ08+g9sVgLy9l3zMa+4zY2HclnXYUBiKZdYG8GRNbQ1cWKf/kZSg5soTgt9dIx/ENxCe+CS3gMLmEx6H2DpIugaDY6hl0q+E9mFtG3a9BV91EUhUNnCoj7ebQ0IYQQ6pCCSgjR4gX6uTGif3tG9G+Pw6lwOquIAyfy+elEHmsOFvKvam8gjvCA/vQLq6aLSx4BVRmUHd1Fyf5vANC5e2MKicYUGo1LWDSmoCi0Jrnq39xlZ2cza9YsCgoKiIyMZNGiRbi71x2cpLq6mjlz5pCeno6LiwuLFi0iKioKRVFYuHAhmzdvRqvV8sorrxAfH4/D4eDll18mLS0NRVGYNGkSDz/8cJOeV1SoN1rNpTmmrlVQ5RSUUVRSJc9PCSGEyqSgEkK0Kjqthk7hvnQK92XCXZ2ocTg5lVnEodMFpJ8uIPVkIZ+U+wF+eLrG0yfUSXePQkKxouSdp/zE7p+PpMEQEIopuCOm4ChMwR0wWtqjNV67+5VoevPmzWPq1KmMHj2ad999l/fee49Zs2bV2Wfp0qW4urqyYcMGdu/ezXPPPcfKlSv56quvOHXqFOvXr+fcuXM88cQTrF+/ns8++4yioiI+//xzKisrmThxIn369KFbt25Ndl4uJj3hgZ6czLz2wBS1z09FyvOBQgihJimohBCtml6npXOEH50j/Bg/pBNOp0JWXimHzxRy/PwFjp+/wOZTThTFB+hMO18NCQFldHS5gNlhpebUvtrnsECDwT8Ed4M3RVXnMQa2x2huh87TT7oLqsBut7N7927effddAMaPH88DDzxwRUG1ZcsWZsyYAUCfPn0oLCwkOzubrVu3MmrUKLRaLZGRkQQHB7Nv3z46depEz5490Wq1uLm5ER4eTk5OTpMWVHDpOaq0IzYURbnqz9fhM4V4uhkIs3g2aS4hhBB1SUElhGhTtFoN4YGehAd6ktwvAoDySjunsi5y4nwRJzOL2JVRxOoCNyAU6EW4h4M4/3KiXIsIVPLRF56ncPPhfx/TxQOjORyjuR2GgDCM5nAMAeHo3L2l0LqNLly4gIeHB3r9pabMbDZjtVqv2M9ms2E2//s5I7PZTG5uLjabDYvFcsX6lJSU2nV79+7lwIEDLFy48DaeydV1CvPh290Z5BdVYvat2/20oqqGXQdziIs2o9XKz5gQQqhJCiohRJvn5mKge1QA3aMCateVVdg5nX2R01kXOZtdzOGci6Se9MFe0w7ojZu2ilifSqI9ywgzFOFbnI8pdxsae0XtMbQu7hj8Qy/98wvB4Bdc+09rMKlwpi3Xhg0bWLBgQZ11ERERVxSsVytgL7/DoygKWq0Wp9N51fW/2L17NzNnzmTRokV4e3vfUN709PTrbk9LS6v3GDVlVQCkbk2ja3jdgur7oyWUVtjpHGhv0LFuxu06bmNrCTklY+OQjI1DMjY+KaiEEOIq3F2vLLIcDifZ+WVs2bkfvZuZc9YSvrOWkJVZRo3DCSh4aSro4F5GJ89yQo0l+BcX4Z6fhq5qc53j6zx8MfgGofcNwuATiN7HUvtfnYcPGo0W8W8jR45k5MiRddbZ7XYSExNxOBzodDry8vLq3HH6RWBgIDabjXbt2gGQn5+PxWIhKCgIm81Wu98v6wE2btzISy+9xOLFi0lMTLzhvLGxsZhMVy+a09LSiI+Pr/cY3e0OPvzmSxSjH/HxXWvX1zicvLvhG7p18Gdc8oAbztYQDc2otpaQUzI2DsnYOCTj9VVVVdV7QexqpKASQogG0um0hAd60rWdG/HxMbXrHQ4n1sJyMvNKybKVkpVXypG8Ujbnl5F/sRIAE3YCdMWEmcqIcK8kyFGGX8FFPKx7MFSXXPaN9Oi9AjB4m9F5mdF7B6D3CkDv5Y/e0x+9lz9ak1tTnnqzZDAYSEhIYP369aSkpLBmzRqSkpKu2G/QoEGsXbuWhIQE9uzZg8lkIiQkhKSkJD799FPGjBlDZmYmZ8+epXv37hw4cICXXnqJDz74gJiYmKt856ZhNOiICPbiREbdgSm+259F3oUKnhzfQ6VkQggh/pMUVEIIcYt0Oi0hZg9CzB7Qte62KruD3PwycgvKyC0sx1pYzpmCMn68UIG1sIyKKgcGavDVluGvKyVAX0aoayWW0nJ8ygrwyDyLsaYUDUqd42qMLug9/NB5+qH39EPn7oPOwxe9hy86Dx+0JXk4ykvQurq36rtdL774IrNnz2bJkiUEBwfz5ptvAvDxxx9js9mYMWMGDz74IHPnzmX06NEYjcba56FGjBjBgQMHuOeeewB49dVXcXFxYcmSJTgcDp599tna7zN9+nTuvvvuJj+/Tj9P8HvkTCFdIv1QFIXVm0/SLsiThJjAJs8jhBDiSlJQCSHEbWT6+S5DRLDXFdsURaG0wk7ehQryLpSTV1RBflEFuRcrSb9YQUFRJQUXK3DU2PHWluOjLcdbW46vtgy/6koCqivxuViAJxm4OsvQKTW1x/YGzu14H7Q6tK5e6N290bl7o3PzQuvmhe7nf1pXT3RunuhcPdG6eqJ19UCrNzbhO3RrQkNDWbp06RXrp0yZUvu1yWTijTfeuGIfjUbDs88+W6dwAliyZEnjB71JE+/qxIGT+Ty/ZAfT74vD083I2Zxinp7cSwajEEKIZkIKKiGEUIlGo8HTzYinm5EOoVcf9EBRFMoq7BRcrORCSSWFxVVcKK7kQkkVR0qqKCq99HVxRRXV5aV4Uo6nthJPbQVemgo8tZV4lFfidbEKb10OHpozuFGJkepr5lL0JgLHPY1H576369RFAwX5u7NoehKv/2M3by7fi4+HiQBvF5J6hakdTQghxM8aVFCtW7eOJUuWUFNTw0MPPcT9999fZ/uRI0eYM2cOZWVlJCQkMG/ePPR6fYNmsBdCCHFtGo0GDzcjHm7Gq97l+k9Op0JJeTXFZdXs3nuQoND2FJdVU1Jeja2smlPl1ZSW2ymtsFNWWoGzshhNZSkGZyUemkrctNW4aapw0diJytAwtHMTnaS4Li93I/Me789fVx9g4w/nePSeWAz61tuNUwghWpp6Cyqr1crixYtZvXo1RqORyZMnk5iYSMeOHWv3mTVrFvPnzycuLo7nn3+elStXMnXq1AbNYC+EEKJxaLUavD1MeHuYsFlMxPcIadDrqu2OS0VWhZ2ySjuVVTV0jfS/zWnFjTDotfx+Uk/G3BlJRND1C2shhBBNq95LXDt37qRfv374+Pjg5uZGcnIyqamptduzsrKorKwkLi4OuDRTfWpqau0M9snJyXXWCyGEaF6MBh1+Xi6EB3oSE+FHXLQFo0GndixxGY1GQ2SItzw7JYQQzUy9BdXlM8xbLJY6M9FfbQZ6q9Xa4BnshRBCCCGEEKKlqrfL39Vmkv/P5Wttv3w/uPoM9tfTkIm1WsJMypKxcUjGxiEZG4dkFEIIIQQ0oKAKCgpiz549tcuXz0QfFBREXl5e7fIvM837+flRUlJS7wz213O9meZBZntuLJKxcUjGxiEZG4faGW92tnkhhBCipam3y9+AAQPYtWsXhYWFVFRUsHHjxjoz0YeGhmIymWqvhK5du5akpKQ6M9gD15zBXgghhBBCCCFaqnoLqsDAQGbOnMm0adMYN24cY8aMoUePHjz22GMcPHgQgEWLFrFgwQJGjBhBeXk506ZNAy7NYL9y5UpGjRrFnj17ePrpp2/v2QghhBBCCCFEE2rQPFQpKSmkpKTUWff+++/Xfh0TE8OqVauueN21ZrAXQgghhBBCiNZAZgYUQgghhBBCiJvUoDtUTU1RFACqq6vr3beqqup2x7llkrFxSMbGIRkbh2S8vl9+f//y+7ytaGj7JT8/jacl5JSMjUMyNg7JeG0323ZplGbY2pWUlHD8+HG1YwghhLhF0dHReHp6qh2jyUj7JYQQLd+Ntl3NsqByOp2UlZVhMBhueO4qIYQQ6lMUBbvdjru7O1pt2+ldLu2XEEK0XDfbdjXLgkoIIYQQQgghWoK2c9lQCCGEEEIIIRqZFFRCCCGEEEIIcZOkoBJCCCGEEEKImyQFlRBCCCGEEELcJCmohBBCCCGEEOImSUElhBBCCCGEEDdJCiohhBBCCCGEuEktsqBat24do0aNYvjw4SxbtkztOFf1l7/8hdGjRzN69GgWLlyodpzreuONN5g9e7baMa5q06ZNjB8/npEjRzJ//ny141zV2rVra/9fv/HGG2rHqaO0tJQxY8aQmZkJwM6dO0lJSWH48OEsXrxY5XSXXJ5xxYoVjBkzhpSUFJ577jmqq6tVTnhlxl/885//5MEHH1QpVV2XZ9y3bx+/+tWvGD16NH/4wx+axfsopP1qbNJ+3Rppv26NtF+No1W0X0oLk5ubqwwZMkS5cOGCUlZWpqSkpCgnTpxQO1YdO3bsUO677z6lqqpKqa6uVqZNm6Zs3LhR7VhXtXPnTiUxMVF59tln1Y5yhfPnzyt33nmnkpOTo1RXVytTpkxRtmzZonasOsrLy5U+ffooBQUFit1uVyZOnKjs2LFD7ViKoijK/v37lTFjxijdunVTMjIylIqKCmXQoEHK+fPnFbvdrjzyyCOqv5+XZzx9+rQybNgwpaSkRHE6ncqf/vQn5cMPP2xWGX9x4sQJZeDAgcoDDzygYrpLLs9YUlKi3HHHHcqRI0cURVGUmTNnKsuWLVM5pZD2q3FJ+3VrpP1q3IzSft2c1tJ+tbg7VDt37qRfv374+Pjg5uZGcnIyqampaseqw2w2M3v2bIxGIwaDgaioKLKzs9WOdYWioiIWL17Mk08+qXaUq/r6668ZNWoUQUFBGAwGFi9eTM+ePdWOVYfD4cDpdFJRUUFNTQ01NTWYTCa1YwGwcuVKXnzxRSwWCwAHDhwgIiKC8PBw9Ho9KSkpqn92Ls9oNBp58cUX8fDwQKPREB0drfpn5/KMANXV1cydO5fp06ermOzfLs+4Y8cO4uLiiImJAeCFF15g2LBhakYUSPvVmKT9unXSfjVuRmm/bk5rab/0age4UTabDbPZXLtssVg4cOCAiomu1KlTp9qvz549y4YNG/j4449VTHR1c+fOZebMmeTk5Kgd5arOnTuHwWDgySefJCcnh8GDB/P000+rHasODw8PZsyYwciRI3F1daVPnz707t1b7VgAvPrqq3WWr/bZsVqtTR2rjsszhoaGEhoaCkBhYSHLli1jwYIFakSrdXlGgD//+c9MmDCBsLAwFRJd6fKM586dw83NjZkzZ3L69Gl69+7dbLtFtSXSfjUeab9unbRft0bar8bRWtqvFneHyul0otFoapcVRamz3JycOHGCRx55hD/96U+0b99e7Th1fPLJJwQHB9O/f3+1o1yTw+Fg165dvPbaa6xYsYIDBw7w2WefqR2rjqNHj/Lpp5+yefNmvvvuO7RaLX//+9/VjnVVLemzY7Vaeeihh5gwYQKJiYlqx6ljx44d5OTkMGHCBLWjXJPD4WD79u384Q9/YPXq1VRUVPC3v/1N7VhtXkv6DEr7dWuk/WpcLemzI+3XrWmp7VeLK6iCgoLIy8urXc7Ly6tzK7O5SEtL4+GHH+aPf/wj9957r9pxrrB+/Xp27NjB2LFjefvtt9m0aROvvfaa2rHqCAgIoH///vj5+eHi4sLQoUOb3dXc7du3079/f/z9/TEajYwfP54ff/xR7VhX1VI+O6dOnWLy5Mnce++9/O53v1M7zhW++OILTpw4wdixY3nhhRdIT09vdleeAwIC6NmzJ+Hh4eh0OkaOHNnsPjttUUv5DEr7deuk/WpcLeWzI+3XrWup7VeLK6gGDBjArl27KCwspKKigo0bN5KUlKR2rDpycnL43e9+x6JFixg9erTaca7qww8/5IsvvmDt2rVMnz6du+66i+eff17tWHUMGTJfDijfAAABx0lEQVSE7du3U1xcjMPh4LvvvqNbt25qx6ojJiaGnTt3Ul5ejqIobNq0ie7du6sd66p69uzJmTNnOHfuHA6Hgy+++KLZfXZKS0t59NFHmTFjBo888ojaca5qwYIFbNiwgbVr1zJ//nxiY2N566231I5Vx5133smhQ4dqu0Nt3ry52X122iJpvxqHtF+NQ9qvxiXtV+Noqe1Xi3uGKjAwkJkzZzJt2jTsdjsTJ06kR48easeq4+9//ztVVVW8/vrrtesmT57MlClTVEzV8vTs2ZPf/OY3TJ06Fbvdzh133NHsblPfeeedHD58mPHjx2MwGOjevTuPP/642rGuymQy8frrr/PUU09RVVXFoEGDGDFihNqx6li1ahX5+fl8+OGHfPjhhwDcddddzJgxQ+VkLUtwcDAvv/wyTz75JFVVVXTp0oVnn31W7VhtnrRfbYe0X41L2q+2o6W2XxpFURS1QwghhBBCCCFES9TiuvwJIYQQQgghRHMhBZUQQgghhBBC3CQpqIQQQgghhBDiJklBJYQQQgghhBA3SQoqIYQQQgghhLhJUlAJIYQQQgghxE2SgkoIIYQQQgghbpIUVEIIIYQQQghxk/5/YLrbHczFrN4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "x_lim = X.interval(.99)\n",
    "x = np.linspace(*x_lim, num=100)\n",
    "\n",
    "axes[0].plot(x, X.pdf(x), label=\"original\")\n",
    "axes[0].plot(x, Y.pdf(x), label=\"recreated\")\n",
    "axes[0].legend()\n",
    "\n",
    "axes[1].plot(x, X.pdf(x) - Y.pdf(x), label=\"error\")\n",
    "axes[1].legend()\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-max-likelihood-fit.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu, sigma = 1.0, 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = stats.norm(mu-0.2, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_samples = X.rvs(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = (X_samples.mean() - mu)/(sigma/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.8338979550098298"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = (X_samples.mean() - mu)/(X_samples.std(ddof=1)/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.9680338545657845"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.9599639845400545"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm().ppf(0.025)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004598401329075357"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * stats.norm().cdf(-abs(z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.003758647967422721"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * stats.t(df=(n-1)).cdf(-abs(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t, p = stats.ttest_1samp(X_samples, mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.968033854565784"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.003758647967422721"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 3))\n",
    "\n",
    "sns.distplot(X_samples, ax=ax)\n",
    "x = np.linspace(*X.interval(0.999), num=100)\n",
    "ax.plot(x, stats.norm(loc=mu, scale=sigma).pdf(x))\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-hypothesis-test-dist-sample-mean.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu1, mu2 = np.random.rand(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.24764580637159606, 0.42145435527527897)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu1, mu2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X1 = stats.norm(mu1, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X1_sample = X1.rvs(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X2 = stats.norm(mu2, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X2_sample = X2.rvs(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t, p = stats.ttest_ind(X1_sample, X2_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.4283175246005888"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15637981059673237"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.24764580637159606, 0.42145435527527897)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu1, mu2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2522c128>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6oH/oKDvdSnP7wL7a7XbSP887mNQZizjW3fekf37KJAwHP2N/yrJzvil80oJpWVLwRchkDF/EPEtXDWh1bOiaQodbwzWTvJhG4VJGp4WbpnrIsqq8XG2i2RGeN3J7M0sxOlsxOprC0p4QJ0nBF7FNCWDpOk5P6lS2tCSyONdPcfLoPcdu0sOXZrgx61X+UmXCMfTRqbP0Zs5GRUNC676RNybEaaTgi5hm7qlDq/h4ubmEDIvCsqIwVNwhSjDCzdO8OH0a/nrQhH+Ef98ETEm4kktIbN0bnoBCfE4Kvohpls4aujWJ7OzO4MqJXvRR+onOTVBYNdlLXY+Ol/ePvL3ezDmYehsxONtG3pgQn5OCL2KW3tOF0d3OJsdULp6eTFFSdKckmJURYHGuj0+PQ2XbyFbX6s3sWxfa1haGvz2E+JwUfBGzzB01+FUte/yTuGlJZrTjAHBZkY+SVHizxojdNfybuH5LGh5bDglS8EUYScEXMUmr+DB1HafcO4HFRRoSLWPjCWOdFr66AHQaeLnahG8E7331ZszC0nUUrW/4j5MKcTop+CImJbka0eNnH9OYmxXet2lHKtUCqyd7aHFqeff48GfRd2TMQqMq2NqrwphOxDMp+CL2qArJznoO+bKZU5yAdnRWIhySyakKF+X52NVsYP8wx/PdSYX4DQkyji/CRgq+iDlqZwM2XBzUT6NkFJ+5H6qlhT4KEgO8ecRIp3cYQ04aLY6MGdjsVaCMrd9iRGySgi9ijrb1MK2BRCYWZUU7ynnptHD9FC86DbzfmHrW/Dqh6M2Yhc7vxtJZE/6AIu5IwRcxxd1lJ0tt46BmIunWaKcJLsmksnKilxa3iS31Q7/Kd6ZNRdHqSWivjEA6EW+k4IuY4m8+gks1YElNjXaUkM3KCDAx0cnHdYYhz7ej6ky4Uif3jePLHPlihMbGs2xChKCz28VkpZZq/TQsxti6Vrk0u5Nmt4XXD5n4Wqn7rDeCkyw6Shh8WghtwXT0e6oo0TZA4sBhLKO3E19nb9D+tSYrOktkFmAXsUMKvogZzsYaNEBC3gR63J5oxxkSs05h1SQPL1aZ+eiEgcuLBxZ3reKl48CuQY/V+rxkAp497+BMnzZgW2JOItoQpke2TJwnBV/IkI6IDc1dPmaoh6jTF2K02qIdZ1gmpyrMy/LzWYOeE92h/9FTDFZ8phRMjvMsoCJECKTgi5jgbKjBrPFjyJsWfOcx7AslXpJNKm8cNuIdwpOWnoRcDK52NP7Y+s1GjC1S8MWYd6IjQCkHadTno7UmRzvOiJh0cM0kLx0eLZ/Uhf4WrseWiwYwyaIoYgSk4IsxTVXB0XAUq9aLLje2r+5PKk5WmJvpZ2uDPuSndvzmVAI6kxR8MSIhFfz169dz9dVXs2LFCp599tmzttfU1HD77bdz7bXXcuedd9LV1RX2oCI+1dhVFmiraNPnoFrPvSZsrLm82ItFD2/VGEN7IUujwWvL6Vv2UB27bxeLsS1owW9ubuaxxx7jueee49VXX+WFF17g8OHD/dtVVeUb3/gGa9eu5fXXX2fGjBk89dRTEQ0t4oOqQk/jcRK1bsidHu04YWUxwBdLvDT06tjVHNrDcp6EXLSKD4OrPcLpxHgVtOBv3ryZJUuWkJKSgtVqZeXKlWzYsKF/+/79+7FarSxduhSAe+65h9tuuy1yiUXcONAKi3WVdOozCVgzoh0n7GZlBChJDvBBrYFOhz/o/l5rNioaGdYRwxa04Le0tJCZeWpxiaysLJqbm/s/19bWkpGRwQMPPMANN9zAww8/jNUaA++8izEtoICjqZYUrRMle3yM3Z9Jo4ErJ3jxK/B/n7YE3V/VGfBZMjD2SsEXwxP0d0lFUdBoTt1YUlV1wGe/38+2bdv485//zJw5c3j88cf56U9/yk9/+tOQQ1RUVIS8b3l5ecj7jgWxlDdSWbNsBjprawfdpjNYaLd3nvX9qg4zlxsq6NCm0uQxgNd+1j7t9lPfy/N4Bnw+U0qC7rzbgwnWfih9nev4BemJbD+iIdPtpDjBff7Gtclkuw7T1dqAX2cm2aJgb3MFz2TNoeXIiZDynyQ/u5ETrbxBC35OTg47duzo/9za2kpW1qnXuzMzMykuLmbOnL41OK+55hrWrVs3pBCzZ8/GZDIF3a+8vJyFCxcOqe1oiqW8kczq62wh2Vk06LYep5d018BfNH0BMJ04SorZiT1vEem29LOOa7fbSU87dRPXZDIN+HymYNuDGcrxg+17Zt7TXZ4CdQEjW9rSmJPvxnCe6fN1Nj04DpNjcOFKySM5OZFEa/DlHS05ORSmhD67qPzsRk448no8niFdKJ8UdEinrKyMLVu2YLfbcblcbNy4sX+8HmD+/PnY7XaqqvpW5dm0aROzZs0achAhTtrdpLLUuJ9uYxY+29ieAjkcdFq47dJsujxatjae/xosYEzEb7BhkmEdMQxBr/Czs7O57777WLNmDT6fj5tvvpnS0lLWrl3LunXrmDNnDv/1X//FQw89hMvlIicnh5///OejkV2MQx4/6NpqSDS7sedcFO04o2ZavpVpaX421xsozQyQZDrHs5qfP55p6Tomi6KIIQvpebDVq1ezevXqAd97+umn+7+eO3cuL730UniTibhU3qCywrifblMuPsvZQznj2ReKfRzu0LHpuIHrp3rPuZ8nIRdr5xGMzhYgZfQCipgnb9qKMaPXC7aOQ9i0Xnw5M6MdZ9SlmFWW5PmpbD//5GpeSyaqRiePZ4ohk4IvxoyttQpLTQfotuTjN8fOAifhdFG+jwSDwqbjhnOvd6LV4bVmYXI0osqiKGIIpOCLMaHFqSG79yAmjQ9vdvxd3Z9k1PUtfl7fq6PKfu7HdTwJueh8TlSnTGMiQicFX4wJW48HuNRchSOhiIAptmfEHKnSrACZFoUPjhsInGPaHI8tBwDFPrRn60V8k4Ivou5op5ap3v3oNQruzPi9uj9Jq+mbXK3Do2XnOebZ6VsUJRmlvW6U04lYJgVfRJWiqmw/7qXMdAhXUgkBoyzDBzAxRaEkOcCndQY853j60mvLQe1qRvHJoigiNFLwRVR9VqtygaYCjQacGTOiHWfM0GjgskIfTr+G7ed4GctjywVUfG1ylS9CIwVfRI3br/LJgS4uNB7BnTIRxSCT7p0uL1FhaqqfrQ0GXL6zt/ss6aA34W0dfJ4iIc4kBV9Ezd8q/Vyi3Y2q1eJMH1/z3YfL0kIfngB81jDIcogaDdq0fLyttfJ4pgiJFHwRFS29CjuqWlloOoY7dTKK3hztSGNSlk1lVkaA7U16egd5+VabVoDqdePvCj69shBS8EVU/GmHjyvNu1B1Bhxp43O++3C5pMBHQIHtjWdf5WvTCgAN3hYZ1hHBScEXo668LkB7UzOzDHXoC2ej6ozRjjSmpVtUZqQHKG/SnzWWrzGY0Kdm45NxfBECKfhiVLn9Kn/a4ePGpN1oDGZ0+TKVdijK8n14FQ3bm86+yjdmFuLvbkNxO6KQTMQSKfhiVP1ljw+bp4USTSOWSfPQ6Ae5GSnOkmVTmZrqZ0ejHs8Zy98aM4sB8LbKW7fi/KTgi1FT3Rrg7aoAt6bvQ2MwYymUt2qHoqzAjzugOevtW11iGlqzTR7PFEFJwRejwhtQefozHzNtdrJ9dVgmzJGr+yHKS1CYkBxga4MB32lv32o0GoyZRfja6lBlURRxHlLwxah4aY+fhm6V27Mq0OiNmItk7H44Li7oe/t2d8vAq3xDZhFqwIfP3hilZCIWSMEXEbf3aBd/O+DnupJuLF3HMBfPRmsIvmi9OFtRkkJhYoDPGvT4T5tJ05ie3zdPvgzriPOQgi8iqsfp5YnXDpObpGGFtQJ0eiwlc6IdK6ZdXOCjx6tlX+up+fI1egOGtFx5PFOclxR8ETGqqvLki7vpdvj45kIX/qYjWIpmojXKW7UjMSFZIdcWYEu9AeW0KRWMmcUEHF0EHLIoihicFHwRMa99VMOWfY3cenkR6e17QavFMmFutGPFPI0GluT76fRo2dNw6vvGrCIAGdYR5yQFX0TE/pp2fv/Gfi6ak8s1pVY89dWYC6ahNcmMmOEwLS1AsknhvSOnBvJ11iR0thSZZkGckxR8EXbtXS5+9sft5KRZ+ecvzcdR8TGoiozdh5FWAxfk+DncDjXtp4q+MasIn70B1T/IfMoi7knBF2Hl9vr58e+34fL4+d5XL8SiV+it+AhjVjE6W0q0440rc7P8mPXwVtWpV28NmUWgKnhl6UMxCCn4ImwUReXx53dxpK6Tb9+2kJLcJHorPkJx92IuKY12vHHHpIeyYg1bjwdod/bdvDWk5qDRG2VYRwxKCr4Imz9vOMCnexv42jWzWDw7F1VV6dr2BoaMQgxpudGONy5dPkmDArxzsO8qX6PVYcgowCeLoohBSMEXYfH6x0f4y3uHuPKiEq5fNgkAV81ufG11JM77AhqNJsoJx6cMm4ZFBVo2Hfbj9vcVeGNmEYrHSaC7PcrpxFgjBV+M2Ic763j61QoumpPLPTeW9hf3rq3r0SWkYp28MMoJx7erputxeOHjmr55dIyZhYA8ninOJgVfjMhnFY089vxOZk1M59u3LUSn7Sv23pbjuI7uIWnR1Wh0+iCtiJGYmqllYrqGDVV+FFVFa7KiT8nC23w02tHEGCMFXwzb1opGfvbH7UwqSOb7dyzGaDj1qn/X9jfR6I0kzb8iignjg0aj4arpepp6VHbX9z2iacyegL+7jYCrJ8rpxFgiBV8My7b9Tfz0j9uZkJfMv3+9DJvl1FTHAbeD3oqPSJi9FJ01MYop48eFRTrSrBo2fH7z1pQ9AQBvk1zli1Ok4Ish21bZxKN/2MaEvGR+eHcZCZaB89r37vsA1e8lacGKKCWMP3qthi9M0bG/SaGhS0FnS0aXmIan+Vi0o4kxJKSCv379eq6++mpWrFjBs88+e879PvjgAy6//PKwhRNjz/bKJh59Zjsl5yj2qqrSvXMjptzJmHInRSllfFo+SY9OC+8e6rvKN2ZPwN/RiOJxRjmZGCuCFvzm5mYee+wxnnvuOV599VVeeOEFDh8+fNZ+bW1t/OxnP4tISDE27DjQzE+e2U5JbiI/+vpFZxV7AHdtJb62OpIWroxCwviWbNGwuEjHRzUB3D711LBOy/EoJxNjRdCCv3nzZpYsWUJKSgpWq5WVK1eyYcOGs/Z76KGH+OY3vxmRkCL6dhxo5pHfb6M4N5Ef3V1GgtU46H7dO99Ga7Zhm3nxKCcUAF+cosPlg83HAn1r3VqS8Mg4vvhc0ILf0tJCZmZm/+esrCyam5sH7PPHP/6RmTNnMneuTH07Hu2sauEnz2yjKOf8xd7f24mjaisJpctlRasomZqppShVwzvVn9+8zSnB116P4nFFOZkYC4I+IK0oyoC3JFVVHfC5urqajRs38swzz9DU1DSsEBUVFSHvW15ePqw+oiWW8g6W9UiTm+c/bCMjycDNS2xUH9h3zuPNRz7Fovg5Yczn+GltZdkMdNYO/hKQzmCh3d45rLztdnv/13kez4DPZ0pJ0J13ezDB2g+lr/MdP5T2T5dsUbC3DSzmC9PNvHI4kY8qGplosGJRFZr2fEJbetuQ2o71n92xLFp5gxb8nJwcduzY0f+5tbWVrKys/s8bNmygtbWVm266CZ/PR0tLC7feeivPPfdcyCFmz56NyRT8irC8vJyFC2Pnrc1YyjtY1r2HW3nhL1spyErikW9cTJJt8Ct7AFUJcGLL0+iLZzNx2cCnc3ydLSQ7iwY9rsfpJd019IfF2u120tPS+j+bTKYBn88UbHswQzl+sH3PzBuufMnJiSRaMwd8LztP5e3jbvZ1ZbD04lw6GvZitB9l4YrbQm431n92x7Jw5PV4PEO6UD4paMEvKyvjySefxG63Y7FY2LhxIz/60Y/6t69bt45169YBUFdXx5o1a4ZU7EVoepxeXG5/8B2HSW9JocXe9zSHxazneGM3P/zdVnLSrfz4nrLzFnsA15Hd+LtaSfvCmohlFKEx6zUsnajjnUMBbncbMGaX4D6+H8XnkaG2OBe04GdnZ3PfffexZs0afD4fN998M6Wlpaxdu5Z169YxZ44sajEaXG4/Ow/wp4CUAAAgAElEQVS2RKz947V1FHf1vSmbaDXy+P/tJDPFwo/vKSM5IXiR6N79LjpbMrapF0YsowjdF6fq2XAwwKbDflblTsBdW4mrZje2aYujHU1EUUiTnKxevZrVq1cP+N7TTz991n4FBQVs2rQpPMlEVLR2uvjd6xWkJ5t55BsXk5oYfMFxf28nzsPlJF+4SubNGSNyk7TMztGy6XCA1TNy0ZoT6N3/iRT8OCdv2op+3Q4vb3xSg9Vs4Mf3XExaUvBiD9Bb8SEoARLnfiHCCcVQXDFVj92psqsRrJMX4Dy0Q57WiXNS8AUAXr/CG5/UEAiofOuW+WSkWEI6TlVVevZswpQ/DWNGQYRTiqGYn68l3arh3Wo/1qkXovq9OKq3RjuWiCIp+AJ/QGF7tYMuh5ery0rIz0wI+VhPffXni5zIlBpjjU6rYflkHRVNCm2GHPTJmfRWfBLtWCKKpODHOUVVeWdrLR29Aa64sIi8IRR7gJ49m9AYzCTMkDdrx6Llk/XoNLBxVysJsy7FdXQPAUdXtGOJKJGCH+c+3dNATUMXM4ssTC5IGdKxitdFb+Un2GaUoTWFNgQkRleKRcOiQh3v727BOK0MVIXeA5ujHUtEiRT8OFZ5tJ29h9uYOyWDiTlDfz7bcWALqtdNkgznjGlfnKqj1x3gszodxqwievd/HO1IIkqk4MepxjYHH+6spzA7gbLSvGG10bNnE4a0PEwF08OcToTTjCwtBRkW3tpylIRZl+KpO4ivszn4gWLckYIfhxwuHxs+O0aC1cCKxcVoT5sbKVTe9gbcJw6QOPfyAXMribFHo9GwcmE21bWdtKWVAtC7/9MopxLRIAU/ziiKysatx/H6FK4uK8FsHN6LUj173gONloQ5l4U3oIiIy0ozMRl1vLW3F1PBdBnWiVNS8OPMtsomGtocXLYgn/Tk4d1oVZUAvXs/wDp5AfrE1DAnFJFgM+tZNr+AD3bWYZhahq+1VpY/jEPyHnwcOd7UTXlVCzNK0phWfO6ZGf0BpX8itUG3H9tJwNGJMumS8+53ktHrx+H0nqMvNXhwERZXlZWwcetxtrsmMEOn73thbsUd0Y4lRpEU/DjhdPt4b/sJ0pPNLJ2ff959Pb4Aew+fe+70vL3vYDYmstedByFM6FaS5KOjqWfQbdnp1qDHi/CYXJDCtKJU/rajlUVTL6S34kPSL78djf7spSrF+CRDOnFAVVXe23ECry/AFRcWo9cN/3+7ztuDrb2S7pyFoNWFMaUYDVeVlXCiuZf2rAtQXL04qrdFO5IYRVLw48C+I23UNvVwcWke6cmhTYh2LkmNO9CoCl25Mg1yLLpkXj4JFgPrj5jQJWXQs0dmt40nUvDHuY5uN5v3NlKck8jsSekja0xVSW7ciiu5BJ8tOzwBxagyGXR88cIitlQ0o592Ka6aPfi6IrfOghhbpOCPY8rnQzl6vZbliwpH/Ly8ufsYRmerXN3HuKsuKiGgqGzzTgGNhp6d70Q7khglUvDHsb2H2mi2O7l0Xj4288hvzCU3bEPRmejJmheGdCJa8jITmDc1k9d3dWGZNJ+ePe+hBnzRjiVGgRT8caqzx8NnFY2U5CYxtXBok6INRuN3k9iym56suah6WRc11l1dNoG2TheNGYsJOLpwVMk8+fFAHsschxRVZdOOWvQ6LZctKAjL1AeJLXvQBrx05ckSebFIVQL4Ok+N1c/P15KeZOTlA1rWJmXQte0NTPlT+7dn2QwD9g+F1mRFZxna9NpidEnBH4f2HW6jsd3JFxYVYrOE5xnr5IateKzZuJOKw9KeGF2qz4O7vnrA974wQeHFPd24503EULuNnt3voU/qu7HfWVtLsrNoSH1YJs6Tgj/GyZDOONPZ2zeUU5yTyLTi8Ex7YHQ0Y+k+TnfehSATpY0bl0/RY9DBO92TQafHdWxvtCOJCJOCP46oqsoH5SfQajRhG8oBSGrYiqrR9r1sJcaNRJOGSyboeP+4Hm3OVDwNh1E8wafKELFLCv44cvB4B/WtDspK80iwGsPTqOInqamc3oxZBIyJ4WlTjBkrp+nxBmCHMgNUBVft/mhHEhEkBX+ccHv8fLq3gZw0KzMnnHtitKFKaD+A3tdLtzx7Py4VpmiZnaPl9Rob+swi3Mcr5RHNcUxu2o4TWyoa8fgCLAvjUA70Def4jUk40qaFrU0RPgFFpeccM5GeTuNXzrnf0hL49Wdw0DCDSb5aumr2o0vIH7C/Qa/DbJS5k2KdFPxxoLHNQeVRO/OmZpKREr7FxPWeLmztVdiLL5eJ0sYof0ChviX4uPuEHC+155ixNBlINZv567F0vpWcTuDYPmpSLKS7Tg0AFOUkSsEfB2RIJ8YFFJUPdtaRYDFwwczwzm+T1LgdDaoM54xzGg0syvFT36un1jIDnd9JskfWvB2PpODHuL2HWrF3u7l0fj5GfRivwFSFpMZtOFMm4bNmhK9dMSaVZvkx6VTesxfiMyWT4TwOqixOM95IwY9hPU4v2yqbKclNYmJecljbttqrMbra6cq/KKztirHJpIO5WX6qOvS0Jc3EFHBi7jkR7VgizKTgx7CPd9cDcOm8869gNRwp9ZvxGxLoyZwT9rbF2LQox4+qwgfdxbh1CdjaKkFVoh1LhJEU/BhV09DF0YZuLpiZTZItTM/cf07tbcPWVklX3hLQyn39eJFiVpmeHmBni4EGy0T0vl7M3bXRjiXCSAp+DPL6A3y8q560JDNzp2SGv4ODHwLQlb8k/G2LMe2ifB/egIbNjhJ8phQS2ipBCUQ7lggTKfgxaEdlM70uH5ctKECnDe/cNhrFD9Uf4ciYhd8cnrl4ROzIsalMTAmwrzORzvQ56PxOrB2Hoh1LhElIv6+vX7+e3/zmN/j9fr7yla9w2223Ddj+7rvv8uSTT6KqKgUFBTz66KMkJ4f3JqLo097lYvehVmZOSCM3wxaWNvOTNaQW2khO8qE9sRvcPZgWLKYkKTxvXCaZoCMsLYnRUJbv48/7zWxz5PNFWy42exWqdzaEa7oOETVBC35zczOPPfYYL7/8MkajkVtuuYXFixczefJkAHp7e/nBD37AX//6V7Kzs/nlL3/Jk08+yUMPPRTx8PFGVfueuTcZdFw0Ozds7RpUL60VW1HS0kitfR/MidjbOqF9R1jaT5k3PyztiNFRmKiQbfbwWb2BRbNKyTq+Ef+xXTDvsmhHEyMUdEhn8+bNLFmyhJSUFKxWKytXrmTDhg39230+Hw8//DDZ2X0v/UybNo3GxsbIJY5jB47ZaWp3cnFpHmZT+G+m6t2dGF3tkDNNpkGOYxoNLMjopturZWdXKq6USSiN1fh77NGOJkYoaNVoaWkhM/PUjcGsrCz27j01b3ZqaipXXHEFAG63m6eeeorbb799SCEqKipC3re8vHxIbUdbuPJ6SOCT3fWkJeowa7o5Xjv4a/LDkVrYNzSkba5EQYsvuZD2hvD94c7zeGi3D95eSoLunNuCOf248/Ux0n5CaT+Uvs53/FDaD6WvkbZfaIVss4ePa3UUF+cwQ3uctt0f4CledO4s1hxajkTn2f14rQtDFbTgK4oyYDIuVVUHnZyrp6eHe++9l+nTp3PDDTcMKcTs2bMxmYKvk1peXs7ChbEzJ3s48/7kmW0EFFh50WTSksxhafOk5CQfdsVLiqcJV3IxVlsi6Wnhe2vXZDKRnjb4DJ7n23Y+7Xb7gOOCtTPcfoZz/GD7npk3XPlCPW6o7bfb7Vw+QeX5A3qOKQXMKfGgqdlOmkWDMbNw0GMsOTkUpmSF3Ee4xGNd8Hg8Q7pQPinokE5OTg6tra39n1tbW8nKGvg/taWlhVtvvZVp06bxyCOPDDmEOL9dB1vYsq+RBdMyw17sT0pz1YGq4EybGnxnERdKkhUKEgN8WqdHyZmO1ppEb+WnqAF/tKOJYQpa8MvKytiyZQt2ux2Xy8XGjRtZunRp//ZAIMA999zDVVddxYMPPhjWqXkFeHwBfvPXvWSnWVk4I7yTo/Xze0hz1eFJyJNFTkQ/jQaWFvro9Wn58JiWhFmXoji7cB7ZGe1oYpiCDulkZ2dz3333sWbNGnw+HzfffDOlpaWsXbuWdevW0dTURGVlJYFAgLfffhvoG6KRK/3weOGdgzS2O7j/toU4PZG5stIe34FO9dMlc96LM5QkK0xKCfDWQR0rpudjyp+Kq2YPptxJ6BPTox1PDFFIj3qsXr2a1atXD/je008/DcCcOXOoqqoKfzLBscZuXn7/MF+4oJDpJWnsPNgS/k6UALrDH+PUJ+OzyB9gcbblxV5+t8fCqxV+bp2zBG9LLb37PiL5ouvQaOTdzVgi/7fGqICi8qsXd2OzGLhj9eyI9ZPYsgeNq5M2a3HE+hCxLcuqUlas4Z1qP21eE7YZF+HvasF9vDLa0cQQScEfozZsPsrB2g7uum522CdH66eqpNa+j5qQSa9Rru7Fua2eoUGnged3+TDlTcGQUYCzehsBV/geDxaRJwV/DGrrdPGHNw8wb2omly0oiFg/1o5qzL0NBKYslRetxHmlWDRcO1vPtlqFfY0KCbMuRUWld9+HqLJQSsyQgj/GqKrKEy/sQlFV/vGmuZF76klVSTv6Ln5jEkqBTH0ggls1Q09uooZndvgImBJJmFGGr70e97F90Y4mQiQFf4zZsOUYu6pbuWP1rLBNjjYYa8chrF01tJd8AXQy570IzqDT8JULDDT3qLxR6cdUMB1jVgmOg1vxd7dHO54IgRT8MaSxzcH/rt/PvKmZXHVRSeQ6UlXSazbgMyXTnSdz3ovQzcnVsaRYx+sVfhq6VRJmL0VjMNGz5z1Uf3hmVxWRIwV/jAgoKo//3050Wg3r/n5+RF9gs9qrsHQfx15yBaqsaCWGaM1CAyYD/PdmL4rBTGLpZQR6O+jc8kq0o4kgpOCPEa9/dITKo3a+fsMcMlMtketIVcg88je85jS6ci+IXD9i3Eq2aLjjQiM1dpXX9/sxZhZhLp5F7973cR6KrUnM4o0U/DGgtqmbP711gCWzc1i+cPCJqcIlqWkHpt5G2iZdLevVimFbXKSjrETHq/v81LQr2KYtwZBRQMvrT+DrbI52PHEOUvCjzOdXeOz5nVhMeu69eV5Eh3I0AR/pNRtwJxbSmzUvYv2I+PDVRQZSLBqe+NiLw68j48qvg6rQ/NdfoPi90Y4nBiEFP8r++GYlh+u6+ObfzSUlMfgU0SORWvs+Bk8XrZNXy3P3YsRsJg3rLjVid6n8ZrMXbVIGmdeuw9tUQ/vbv4t2PDEIKfhRtG1/E69+eIRrLp7ARXPyItqX3tVO2vH36Mmaiyt1UkT7EvFjcoaWNQsN7G5QePGjOmxTLyCl7EZ6dr9Lz55N0Y4nziCDuFHS0uHksed3MqkgmTuunRXx/rIOvQYaLa2Tr414XyK+fGGKjsPtfQU/Ly+Ty5fdgrvhEG0bnsaQUYg5f0q0I4rPyRV+FHh8AR79w3YCisp3bl+EQR++1aUGY2vbT0LbftpLrsBvToloXyL+aDQa7rrQQOmEZJ54cTflB9vIvv4+dAkpNP/lp/i7WoM3IkaFFPxRpqoqv35pD4dPdPL/3bqAvIyEiPan9bnIrnoJjy2XjsKlwQ8QYhj0Og3f+buplOQm8dM/budAk4+cv38Axe+l6cWfoHic0Y4okII/6t745Cibdpzg1hXTWDw7N+L9ZR5+HZ2vl6YZX5LHMEVEWU16frB2CVmpFh5++jMq2k1k3/htvK11NL/yGKoSiHbEuCcFfxRtq2zif17bx+JZOXzpisivLmVrqyS5cRsdRZfhSYrs8/1CAKQmmnn0Hy+hIDOBH/3vVnb2ZJCx8i5cR3bS/s7vZWbNKJOCP0oOnejg53/awcT8ZL5920K02sg+FqnzdJFz4HncCXm0l6yIaF9CnC45wcQj/3gxUwpT+Nkfd/B6axFJF66me8dbdH78l2jHi2tS8EdBY5uDH/5uK8k2I/925xLMpggPragKufufQxPw0zjrdlSdIbL9CXGGBIuBR75RxhUXFvHCO9X8+vg0TDOW0vHxC3RuXR/teHFLCn6EtXQ4efC/PyUQUHj4riWkJpkj3mfGkb9h7TxMy7Qb8NmyIt6fEIMx6HX809/P4+4b5rCruo0H9kzBkzcf+7vP0L3r3WjHi0tS8COo2xngod9sxuny8cO7yyjKSYp4n4lNO0mr/YDO/DK6cy+MeH9CnI9Go+GaSyby2H3LSE6y8L2KmTSaJ9L25n/TW/FxtOPFHSn4EdJsd/LMu6109Lj5wdqLmFwQ+effLZ01ZFe9gDNlIi1Tro94f0KEqiQ3if/852XccuUsnmy9mCP+LJpf+yXNW96MdrS4Is/pRUBtUzff/+0WnJ4AP7rnEqaXpEW8T2NvA3l7f4fPnEbD7K+ANrIvc4n4ElBUepznnxBNcfvx2s//vP3lCwuZNyWTV97LwF37IrM2/Y639tRQvOIWMlKsAFjMehKtxrBlF6dIwQ+zPYda+dkft6PXafnaFVmjVOybKNj9FIrORP28r6MYI/syl4g//oBCfcv5i3lqqoNj3aHNkjl/ZgEdeXdTtedZpre/z/u/b2Jn4nJmTcrghmWTpOBHiBT8MPrbp0d56tV95Gcm8G93Lqb+WFXE+zT11JO/+7eg0VE372785tSI9ylEOKSm2GDpXTQfeIXlTZtJd7n50+YlbNnbyBWLi7h0Xj4luUkRnTI83kjBDwOn28dvX9nHph0nuGBmNt++bSFWs4H6Y5Ht19peRW7Fn1D0ZurmfwOfNSOyHQoRbhotXTNuRGtLZc6RN/l+ros3Tav466ZD/OW9Q+Rm2Li4NI+LS/OYVJAsxX+EpOCP0MHjdv7z2Z002x3cumIaf3/FNHQRfqkKVSWl7hMyD7+O15ZNfemdcmUvYpdGQ0fx5XhtueRU/plb3M9z1613sdNTzKd7G3j5g8O8tOkQmakWFk3PZtHMbEonZ2A2SvkaKjljw+Rw+fjTWwd4c/NRMlMsPHrvJcyckB7xfrU+J9lVL5LYuo/ejJk0zrwNVR/5Z/uFiDRHxgyOX/AvTD7yf/S+9QQL5izjijVfw6GY2FrRyNb9TbxffoK3thzDqNcyZ3IGF8zIxhTwRzt6zJCCP0T+gMI722p5/u0quno9rLp4ArdfNQOrObJvs6qqSkLLHrKqX0Hnc9Iy+Vo6Cy8FjTxZK8YPvyUdy/Xfx1D5Nzo3v4KrZg9pl9/OFy9cyhWLi/H5A+w70s6OA83sqGzmv6v2AfDy1veYPzWLeVMzmT0pA0uk32aPUXJWQuTzB/hoVz0vvFtNY5uDGSVpfP/OxUwpjPxQiqfpKO6NfyDvxD7cCfnUz70LT2JBxPsVIho0Oj1py/4B2/SLaHvzv2ld/yTd5RtIu+xWzCVzWDAtiwXTslh73Wwa2hy8snEHzb1GNmw5xusf16DXaZhWnMb8qZnMn5bFpIKUyA+zxggp+EE0251s2nGCtzYfpaPHQ0luEt+/YzEXzMyO+A0kd301XZ+9hqNqK5isfVf1BZfIM/YiLpiyS8j76k/o3fcR9g+epfG5f8dcOIPkxauxTlmERqsjPzOBi6YnsnDhQry+AJVH29ld3cqu6lb+vKGKP2+owmYxMHNCGrMnpjNrYjqTClLQ6+LzN2Mp+INosTvZVtnE5r2N7DvSBsCC6Vnct3QS86ZmRrTQ+3vsOA5uo2fPJrxNR9CabaRcfCO+aVfQecwRsX6FGIs0Gi2JpZdhm1lGz6536frsNZpf+jn6pAxsMy8mYUYZfD7lstGgY97ULOZNzeKrQFevhz2HWtlzqI39NW1sr2wGwGTUMa0olSmFKUwpTGVyYQpZqZa4eAIopIK/fv16fvOb3+D3+/nKV77CbbfdNmD7gQMHePDBB3E4HCxatIh///d/R6+Pjb9LFEWloa2Xw3VdVNa0U1HTxonmXgAKshL48pXTuWxhIdlp1sj073XjaarBVbMb5+GdeJuPAmDMKiF9xZ0kli5Ha7LQYncCUvBFfNLqjSRfcDVJC1fiqN5Gz+5NdG17g67PXiPJkkJbxyWYC6ZjLpiOPrFvmDU5wcTS+QUsnd83/NnR7abyqJ2Kmjaqjtl57aMj+AN9f1kk2YxMzEumMCeRwuxECrMSKMxOJDnBFLX/5kgIWpWbm5t57LHHePnllzEajdxyyy0sXryYyZMn9+9z//338+Mf/5h58+bxwAMP8OKLL3LrrbdGNHiofP4A3Q4v3Q4vnT0emu1OmtodNLU7abI7qG/pxe3tW4nHatYzc0I6KxYXc+HMHPIyw/PGqur34e/twN/dir+rDX9XK97WWrzNR/G1NwIqaLSYC6eTtvzLWCcvwJhVHJa+hRhPNFodCdMvImH6RQRcPTirt9Pw2Vv07NxI97Y3ANAnZ2HMmYAhLRdDai6GtFz0iWkk25IpK83l4rl5QF9tONbYzeETnRw60cmxxm7e2Xq8vx5AX03ISrWSkWIhK9VCZqqVlAQTKYkmkmxGkhP6/m026mLiN4SgBX/z5s0sWbKElJS+yb9WrlzJhg0b+OY3vwlAfX09brebefPmAXDjjTfyxBNPhFTwT65+4/WG9jo2gMfjAaDH6eWvmw7hcPnw+hV8fgW/X8EbCODzqfgCARwuHx7v2cuq6bQaMlIs5KRZmDc5jaLsRIpyEsnLTBhwc+dkX+cScHbRuflVFI8TNRBAVf0QCKAG/Kh+D4m9XRz+5CnUgO+sY/WJaRiyJ5MwezmGjEJMeZPRmfp+i1AH6dvv86IlMkvEKYqCzmiCz38rC2h0/V+Hg19RztnecPs6PW+wPkbST6jtB+vrzLwjaT9YX+Fo/8y8ofSjKEpYfkb9Pi8eTwj3qbRGjNMvptefzKwZ0/G2nsDTVIO3qQZ3ez09dYfgjGUVNVo9WksCWoMJjd6IUWdglsHAHL0Bw7x8kpdch73bTWObk4a2Xto6Xdi73LR1u9h1sBOX+9yPgJoMOkxG3cB/G3RodRq0Wg1aNGi0Gnp6utl8aAc6nYYrLyohfxgXlidr5lBXEAv6E9DS0kJmZmb/56ysLPbu3XvO7ZmZmTQ3N4fUuc/XVwirq6tDDlxRUdH/9aISGPltCB9gp6vVTlfrMA7PWTjC/ukbqTlUE3S39AhNL+LyQtac+f2fuwFjYvjab+5xYSycOOi24faVdcaKjefrYyT9hNp+sL7OzDuS9oP1FY72z8wbSj8ub29YfkYb6zpprBvaMfsPfD6NiT4bCrJhmA+x1e3f3/91nq3vH/L1QOLn/4TDqSf7OpqP0RFauRyUz+fDbA79PZyg1VJRlAG/qqiqOuBzsO3nY7PZmDp1KgaDISZ+HRJCiLFAVVV8Ph82m21IxwUt+Dk5OezYsaP/c2trK1lZWQO2t7aeujRua2sbsP18tFotiYlhvJQUQog4MZQr+5OCPoxaVlbGli1bsNvtuFwuNm7cyNKlS/u35+fnYzKZKC8vB+C1114bsF0IIcTYoFFDGPVfv349v/3tb/H5fNx8882sXbuWtWvXsm7dOubMmUNVVRUPPfQQvb29zJo1i0cffRSjUeazFkKIsSSkgi+EECL2xef7xUIIEYek4AshRJyQgi+EEHFCCr4QQsSJmCj4jz/+OE8++eSg2+rr65k/fz7XXXcd1113HXfeeecopxvofFm9Xi/3338/V111FTfccANHjhwZ5XSnNDQ0cNttt3HllVfyjW98A4fj7InZxsK5Xb9+PVdffTUrVqzg2WefPWv7gQMHuPHGG1m5ciUPPvggfn90Vz8KlvdXv/oVy5cv7z+ng+0zmnp7e7nmmmuoqzv71daxdm7h/HnH2rn91a9+xapVq1i1ahU///nPz9oelfOrjmHd3d3q9773PbW0tFR94oknBt1nw4YN6ve///1RTna2ULL+z//8T3/Wbdu2qX/3d383mhEH+PrXv66+8cYbqqqq6q9+9Sv15z//+Vn7RPvcNjU1qcuXL1c7OjpUh8Ohrl69Wj106NCAfVatWqXu2rVLVVVV/d73vqc+++yz0Yiqqmpoee+++251586dUUo40O7du9VrrrlGnTVrlnrixImzto+lc6uqwfOOpXP76aefql/60pdUj8ejer1edc2aNerGjRsH7BON8zumr/Dfe+89SkpK+NrXvnbOffbt20d1dTXXXXcda9as4eDBg6OY8JRQsn7wwQdce+21AFxwwQXY7XYaGhpGK2I/n8/H9u3bWblyJdA34d2GDRvO2i/a5/b0ifusVmv/xH0nDTZx32D/HaMlWF7omwvqt7/9LatXr+aHP/xh0An6IunFF1/k4YcfHvTN+LF2buH8eWFsndvMzEy++93vYjQaMRgMTJo0acCf9Wid3zFd8K+//nq+/vWvo9Ode+Y8k8nEtddeyyuvvMKdd97JvffeO6TZN8MllKyDTTTX1NQ0GvEG6OjoICEhoX/NgnNNeBftczvYxH2n5xzJxH2RECyvw+FgxowZ3H///bzyyit0d3fz61//OhpRAXjkkUdYtGjRoNvG2rmF8+cda+d2ypQp/cX82LFjvPXWWyxbtqx/e7TO75hYpeStt97i0UcfHfC9iRMn8swzzwQ99p/+6Z/6v162bBn/+Z//SU1NDdOnTw93TGBkWdUzJpZTVRWtNrJ/5w6Wt7i4+KzJ6gabvG60z+2ZIjlxXyQEy2Oz2Xj66af7P99xxx088MAD3HfffaOaMxRj7dwGM1bP7aFDh7j77rv5zne+Q0lJSf/3o3V+x0TBv+qqq7jqqquGdeyf/vQnrrnmGlJT+6YcVVU1oqttjSRrdnY2LS0tFBUVAUObaG64Bsvr8/lYvHgxgUAAnU531oR4J432uT1TJCfui4RgeRsaGti8eTM333wzMPrncyjG2rkNZiye2/LyctatW8cDDzzAqlWrBmyL1vkd00M6odi+fTsvvfQSANu2bUNRFCZOHBblRS4AAAF9SURBVPq84qNh2bJlvPbaawDs2LEDk8lEXl7eqOcwGAwsWrSIN998E4BXX3110Anvon1uY23ivmB5zWYz//Ef/8GJEydQVZVnn32WK664Imp5z2esndtgxtq5bWxs5N577+UXv/jFWcUeonh+I35bOAyeeOKJAU++PPfcc+rjjz+uqmrfkxFf/epX1VWrVqk33nijeuDAgWjFVFX1/Fndbrf6ne98R7366qvV66+/Xq2oqIhWTLWurk798pe/rF511VXqHXfcoXZ2dp6Vdyyc29dff11dtWqVumLFCvWpp55SVVVV77rrLnXv3r2qqqrqgQMH1JtuuklduXKl+i//8i+qx+MZ9YynC5Z3w4YN/du/+93vRj2vqqrq8uXL+596Gcvn9qRz5R1L5/ZHP/qROm/ePPXaa6/t/+e5556L+vmVydOEECJOxPyQjhBCiNBIwRdCiDghBV8IIeKEFHwhhIgTUvCFECJOSMEXQog4IQVfCCHihBR8IYSIE/8PoXv+l/A1h6oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(X1_sample)\n",
    "sns.distplot(X2_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nonparameteric methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = stats.chi2(df=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_samples = X.rvs(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kde = stats.kde.gaussian_kde(X_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kde_low_bw = stats.kde.gaussian_kde(X_samples, bw_method=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 20, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rob/miniconda3/envs/py3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
    "\n",
    "axes[0].hist(X_samples, normed=True, alpha=0.5, bins=25)\n",
    "axes[1].plot(x, kde(x), label=\"KDE\")\n",
    "axes[1].plot(x, kde_low_bw(x), label=\"KDE (low bw)\")\n",
    "axes[1].plot(x, X.pdf(x), label=\"True PDF\")\n",
    "axes[1].legend()\n",
    "sns.distplot(X_samples, bins=25, ax=axes[2])\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"ch13-hist-kde.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.10979087,  0.4379679 , 14.20879078,  5.94683846,  1.78490438,\n",
       "         5.58416739,  4.18349885,  2.78527976,  0.68112826,  7.7643985 ]])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde.resample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _kde_cdf(x):\n",
    "    return kde.integrate_box_1d(-np.inf, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kde_cdf = np.vectorize(_kde_cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 3))\n",
    "\n",
    "sns.distplot(X_samples, bins=25, ax=ax)\n",
    "x = np.linspace(0, 20, 100)\n",
    "ax.plot(x, kde_cdf(x))\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def _kde_ppf(q):\n",
    "    return optimize.fsolve(lambda x, q: kde_cdf(x) - q, kde.dataset.mean(), args=(q,))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kde_ppf = np.vectorize(_kde_ppf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.39074674, 11.94993578])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde_ppf([0.05, 0.95])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.14547623, 11.07049769])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.ppf([0.05, 0.95])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%reload_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>IPython</td><td>7.5.0</td></tr><tr><td>OS</td><td>Darwin 18.2.0 x86_64 i386 64bit</td></tr><tr><td>numpy</td><td>1.16.3</td></tr><tr><td>scipy</td><td>1.2.1</td></tr><tr><td>matplotlib</td><td>3.0.3</td></tr><tr><td>seaborn</td><td>0.9.0</td></tr><tr><td colspan='2'>Mon May 06 15:41:15 2019 JST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE\\_401/final)] \\\\ \\hline\n",
       "IPython & 7.5.0 \\\\ \\hline\n",
       "OS & Darwin 18.2.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "numpy & 1.16.3 \\\\ \\hline\n",
       "scipy & 1.2.1 \\\\ \\hline\n",
       "matplotlib & 3.0.3 \\\\ \\hline\n",
       "seaborn & 0.9.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Mon May 06 15:41:15 2019 JST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]\n",
       "IPython 7.5.0\n",
       "OS Darwin 18.2.0 x86_64 i386 64bit\n",
       "numpy 1.16.3\n",
       "scipy 1.2.1\n",
       "matplotlib 3.0.3\n",
       "seaborn 0.9.0\n",
       "Mon May 06 15:41:15 2019 JST"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information numpy, scipy, matplotlib, seaborn"
   ]
  }
 ],
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   "display_name": "py3.6",
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